In an effort to create a consistent system for dealing with sexual-assault cases on State University of New York campuses, Gov. Andrew Cuomo on Thursday announced an initiative to define sexual consent that he said may become a state law.

The new policy, passed unanimously by SUNY’S trustees, calls for all SUNY campuses to adopt a uniform definition of consent as “given by words or actions”—not simply the absence of “no.”

“Silence, in and of itself, cannot be interpreted as consent,” the SUNY resolution says, and “consent to any one form of sexual activity cannot automatically imply consent to any other forms of sexual activity.”

Sexual assault has become one of the most talked-about issues on campuses across the country, with groups of students protesting school policies that they say have failed to keep them safe or hold rapists accountable.

“New York is taking on a difficult, uncomfortable topic…SUNY can lead and reform,” said Mr. Cuomo.

Earlier this week, California Gov. Jerry Brown signed a law requiring colleges and universities that receive state funds to adopt a rule termed “yes means yes” that requires affirmative consent, much like the new SUNY policy.

While Mr. Cuomo’s policy now applies only to SUNY campuses, the governor said Thursday that “if it goes well on the SUNY system, then we will codify it and hopefully pass it as a law in the state so it’s then imposed on all schools, public and private.”

The new SUNY policy also grants immunity for drug and alcohol violations for students reporting incidents of sexual violence and says that all SUNY campuses will conduct surveys on the topic.

Mr. Cuomo, a Democrat up for re-election, so far has bipartisan support for the measure.

“We…support the creation of a uniform model to prevent sexual assaults from occurring on SUNY campuses,” said Sen. Dean Skelos, a Long Island Republican.

A spokesman for Sen. Kirsten Gillibrand, the New York Democrat sponsoring a bill to overhaul campus sexual assault policies nationally, said: “We commend Gov. Cuomo for taking a leadership role at the state level as we continue efforts in Congress to pass critically needed bipartisan legislation.”

On SUNY campuses, there was some skepticism over the policy.

“I can see why they would do that, but I don’t know how practical that would be,” said Gabriel Rivera, a freshman at SUNY Binghamton who said sexual assault has been widely discussed on campus this semester.

The affirmative-consent policy “may not be completely feasible in certain circumstances,” he said, “but it’s going in the right direction.”

Write to Mike Vilensky at