The Gemara Gitin 71a states that it is not acceptable to submit testimony in writing. This is derived from Devarim 17:6 where the Torah tells us that the decision is made "according to the mouths of 2 witnesses". The Gemara explains that this means that the testimony must come from their mouths, and not from their writing.

Dovid Bloom

(This question is on Rabeinu Tam, cited in Tosfos to Yevamos 31b, DH d'Chazu, who says that the custom now is that the witnesses send their testimony in their handwriting to Beis Din. He explains that the Gemara in Gitin 71a, cited above, refers specifically to a mute person. Since he is unable to give testimony even if he would go to Beis Din, it is not possible to accept his testimony in writing. In contrast, somebody capable of testfying in Beis Din is allowed the convenience of sending his testimony in writing to Beis Din.)

1) I found, bs'd, that the Teshuvos Tzemach David (by the author of Mikdash Dovid, Rav David Rappaport zt'l Hy'd) at the end of #29 asks this question. He answers that Rav Yonasan Eibeshitz in Urim v'Tumim (Urim 28:29 and Tumim 28:15) writes that for capital cases Rabeinu Tam agrees that it is not sufficient to write down one's testimony. This is because for capital cases the witness must give his testimony personally in front of the accused.

2) I found, bs'd, a different answer to this question in the Sefer Divrei Mordechai (Pesachim #64, page 178, DH v'Chen) by Rav Mordechai Leib Man zt'l.

The thinking behind this is that the very fact that written testimony is acceptable in Beis Din is itself the reason that writing the name of Hash-m that they heard is also considered Megadef, since, according to Rabeinu Tam, writing is equivalent to speaking.

The Divrei Mordechai bases his answer on what the Noda b'Yehudah (first edition, YD #66 (DH Michtavo) and CM #30:11) writes concerning the question of whether or not an oath taken in writing is considered an oath. He writes that the Torah states that one has to "tell" the testimony, which usually means that one must speak, but according to Rabeinu Tam it is sufficient to write it down. This means that, according to Rabeinu Tam, writing is equivalent to speaking. It follows that a written oath is also an oath mi'Oraisa according to Rabeinu Tam.

The Divrei Mordechai takes this one step further and suggests that Megadef in writing is also a full-scale Megadef, so there is no difference whether the witnesses say what they heard or write it down. In both ways it is Megadef mid'Oraisa and writing down their testimony will not make it a lighter prohibition.

3) If the witness cannot give oral testimony, due to the prohibition of Megadef, this is equivalent to a mute person, who -- Rabeinu Tam agrees -- may not send written testimony:

I found, bs'd, another beautiful answer in Sefer Derech ha'Melech (by Rabbi Dov Berish Rappaport zt'l, 1824-1906) on the Rambam (Hilchos Avodah Zarah 2:9, page 69, DH v'Hineh Lich'orah). We should note that Tosfos (Yevamos 31b, DH d'Chazu), which is the source of the Din of Rabeinu Tam, writes that the reason why a mute cannot send his written testimony to Beis Din -- and is different from the person who is physically capable of going to Beis Din but merely wants to make life easier for himself by sending written testimony -- is because of the rule, "Kol she'Eino Ra'uy l'Vilah, Bilah Me'akeves" (Menachos 103b). If a person is physically capable of doing something, then he does not have to actually do it, but he may take an alternative route. In contrast, if he is physically incapable of doing it, then the alternative route is not an option and it will not help. The mute person could not come and speak in Beis Din even if he wanted to, so he does not have the option of sending a letter instead, while the healthy person could come and speak in Beis Din, so we say that if he wants to save himself the bother of doing so, it is acceptable if he sends a letter.

The Derech ha'Melech continues the logic and asserts that if a person is prevented from saying something in Beis Din because of a prohibition, this is equivalent to him being prevented by a physical disability. His proof is from Tosfos in Gitin (28b, DH v'Ha). The discussion there concerns the Mitzvah of leaning on the animal offered as a sacrifice (Semichah). We know that Semichah is a Mitzvah but the lack of doing it does not render the sacrifice invalid. Tosfos asks (four lines from the end of Tosfos) that the Korban of an uncircumcised or Tamei person should be invalid because of the lack of Semichah. This is because even though the lack of Semichah does not make a Korban invalid, that is only when one could have done Semichah but omitted it, while if it was not possible at all to do Semichah, then the lack of it will make the Korban invalid due to the rule of "Kol she'Eino Ra'uy l'Vilah, Bilah Me'akeves."

Now an uncircumcised or Tamei person is physically capable of doing Semichah but he is Halachically incapable of doing it. The Derech ha'Melech proves from this that there is no difference between being physically incapable or Halachically incapable of doing something. It therefore follows that if there is a prohibition against saying verbally the name of Hash-m used by the Megadef, then this is equivalent to a mute person who cannot physically say the Name, so he can also not send the Name on a piece of paper.

(I am reminded of a story about Rav Moshe Feinstein zt'l who was once asked, during Tefilah, to come outside the Beis Midrash for some reason. Rav Moshe had finished his Shemoneh Esreh but there was someone who was still in the middle of Shemoneh Esreh. In order to leave the Beis Midrash, Rav Moshe would have had to walk in front of the person still davening. Rav Moshe said, "I cannot walk there. There is a wall there!" Of course, there was not a physical wall but there was a Halachic wall, since the Halacha states that one may not pass in front of someone in the middle of Shemoneh Esreh.)

Dovid Bloom

The Netziv of Volozhin writes that is better that the Sanhedrin should not see the Name that the Megadef said:-

Teshuvas Maishiv Davar 4:53 DH Reishis (by the Netziv) asks why someone does not write down the Name that the Megadef used, and all the witnesses would say "this is what we heard"?

Maishiv Davar answers that possibly it is better that one of the witnesses should say explicitly the Name that he heard, rather than the entire Sanhedrin seeing the Name, that was used as Giduf, written down.

He cites the verse in Ezra 4:14 " It is not fitting that we should see the dishonor of the king".

If one sees, written down, the Name of Hash-m that has been used for Giduf, this is a dishonor for Hash-m.

It is more of a disgrace that this is in writing for all to see, than if it is merely said by one of the witnesses, and the others merely confirm that this is what they heard.

Dovid Bloom

Chasam Sofer says that Megadef done in writing is a more severe transgression than if done orally:-

I want to present here, bs'd, the position of Teshuvas Chasam Sofer Choshen Mishpat #79 DH veGam, but before I do so, we should look at Teshuvas Chavos Yair #194 DH veKol, which is cited by Chasam Sofer.

There is quite a lot of discussion in the Poskim about the relative power of speaking and writing in Halacha, which is one of the reasons why the question about why did the witnesses in Sanhedrin 56a not write the Name they heard from the Megadef instead of saying it, comes up quite a bit.

Chavos Yair asserts that if somebody writes down his oath this is a full-scale oath. He notes that there is a hint for this in the Book of Ester 8:8 "for writing which is written in the name of the king, cannot be reversed". Writing is much more permanent than the "hot air" of merely speaking. Chavos Yair adds that "writing" is also considered more of an action than "speaking" and states that if someone writes in his notebook that he will donate a sum of money to charity this is as if he said it.

Chasam Sofer asks our question explicitly:- why did the witness have to say the Name of Hash-m and cause everyone who heard it to rend their garments? Would it not have been better to write it down?! Chasam Sofer answers according to the principle expounded by Chavos Yair; writing is considered an action whilst speaking is not considered an action. Therefore it is a more serious prohibition to write the Name of Hash-m uttered by the Megadef than to say it, which is why the witnesses were instructed to say it.

Dovid Bloom

If the witnesses would write the Name this would require Genizah and might be a negative reminder of the Megadef for posterity:-

To conclude this topic I would like, bs'd, to offer my own suggestion why the Name of Hash-m was not written down, but was said. This is based on ideas that I got from the aforementioned Chavos Yair and Maishiv Davar and took a little further.

Chavos Yair stresses that writing is "Miskayem"; lasting. I suggest that this is exactly what we do not want. Clearly, after the case of the Megadef was finished, the Name of Hash-m that would have been written down requires placing in Genizah. It could remain there possibly for hundreds or even thousands of years (and there is a possibility that it's holiness would not always be respected).

Maishiv Davar writes that we do not want the entire Sanhedrin to see the Name of Hash-m. I add to this that since it is placed in Genizah it might be seen by later generations long long afterwards. This would be much worse.

And I cite further an idea from the Rambam, on a slightly different matter, which I think is relevant here too. This is from Rambam Hilchos Yesodei HaTorah 6:8, who writes that a Sefer Torah written by a heretic must be burnt in order that no remembrance should be left of the heretics or their deeds. There is a similar thinking that can be applied to the case of Megadef. The witness who wrote down what he heard is clearly not a heretic, so we could definitely not burn the Name that he wrote. But, on the other hand, Lecatchilah we do not want this Name written down, because it reminds us of a very negative episode where somebody else cursed Hash-m. This is why we prefer to have the witness merely saying the Name of Hash-m that he heard, since that way we will forget about this entire painful incident as soon as possible.

Dovid Bloom