NEW YORK — A “yes means yes” provision and other protections against sexual assaults on campus would be expanded to New York’s private colleges and universities under a law proposed Saturday by Gov. Andrew Cuomo.

The governor said the bill would combat sexual abuse “and the imbalance of power that women face across the board.” It would expand policies in effect since last year at the state’s public university system.

“It’s worked very, very well,” at the State University of New York, the governor said. “We now want to codify it as a law.”

The bill would require that a woman give “clear, unambiguous, and voluntary” consent before any sexual activity. To encourage victims to come forward, students reporting assaults would get immunity from related offenses such as drug use. And victims would be offered the option of reporting an assault to state police rather than campus authorities or a local police department.

“You have my word,” the governor said, that state police “will handle this professionally and will understand who the victim is.”

Calls and emails to several private colleges were not immediately returned. A Cornell University spokeswoman said the college was “unable to provide a comment” on Saturday.

California has had a similar law since September that applies to any college that receives state money for student financial aid. Cuomo said he felt the New York measure would “go nationwide” if it became state law.

“When you do something in the State of New York, people notice,” he said, predicting it would “start a dialogue across the nation.”