The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with blank check
Unrestricted authority, a free hand, as in I'll support most of the chairman's agenda, but I'm not ready to give him a blank check for the company's future. Literally this term signifies a bank check that is signed by the drawer but does not indicate the amount of money, which is filled in by the person to whom it is given.
[ Late 1800s