Green’s Dictionary of Slang

(US Und.) silent, e.g. under interrogation.

1930		D. Hammett Maltese Falcon (1965) 358: ‘You’ll be hearing from Dundy again. Stay dummied up on him and you’ll be all right’.
1942		R. Chandler High Window 107: ‘How long do you expect to stay dummied up?’ he asked. ‘I don’t know’. ‘Let me help you out. I give you to to-morrow noon [...] I give you till then to [...] decide to come clean.’.