HACKENSACK, N.J. — A bill that would bring a “zero-tolerance” policy on bullying to New Jersey public schools easily passed both houses of the state Legislature on Monday.

The legislation was introduced earlier this month in response to the suicide of Rutgers University freshman Tyler Clementi, 18, of Ridgewood.

The recent Ridgewood High School graduate jumped to his death from a bridge Sept. 22, after his roommate allegedly streamed sexual activity with a man to Internet viewers via a Web camera.

Last week, lawmakers in the Assembly and Senate Education Committees listened to several hours of testimony from students and parents who detailed their personal experiences with bullying in New Jersey schools.

The anti-bullying measure now heads to Gov. Chris Christie’s desk for consideration.

New Jersey enacted an anti-bullying law in 2002, but Assemblywoman Valerie Vainieri Huttle, a Democrat, and other sponsors of the new bill said more must be done to clarify exactly what schools should do to discourage and punish bullying.

The legislation passed Monday would make it clear that New Jersey has a “zero-tolerance” policy, Vainieri Huttle said.

The legislation would require public school teachers and staff to receive training in suicide prevention and dealing with incidents of bullying. It also requires school districts to establish anti-bullying programs.

The measure would also designate a “Week of Respect,” starting the first Monday in October, to focus on preventing harassment, intimidation and bullying.