Say nothing - especially in circumstances where saying the wrong thing may get you into trouble.
This probably derives from the German word stumm meaning silent. The phrase keep schtum (variously spelled 'keep stumm', 'keep 'keep shtoom', 'keep schtum' etc.) is British and fairly recent. It has the sound of a Yiddish phrase but it is more likely that it originated in the UK criminal community. The earliest citation of it is in Frank Norman's, book Bang to rights: an account of prison life, 1958:
"I think it's much better to keep shtoom."
"You can always shtoomup if any screws are earholeing."