Going through the L. Jean Carroll docket, I came across this bit from the SDNY jury instructions where the foreperson has to "clutch the envelope [with the completed verdict form] to your heart" when returning it to the courtroom.

(Both sides included the same language in their proposed instructions.)

I've been a juror in SDNY several times (way back when, long before the Kevin Spacey case they cite), once as the foreperson, and I definitely don't remember this.
@mattblaze every time I've been a juror, its been either really boring, or really horrible, but I would do it again!