The Cambridge City Council last night voted to ask the state legislature for permission to enact measures to offset the effects of Proposition 2 1/2 on the city.

The measures--which include an end to the exemption from the property tax granted local colleges and universities--were approved 6-2, despite efforts by several councilors to win unanimous approval.

State legislators will probably not consider the package for several months, and even then are unlikely to support the home rule petitions, Councilor Saundra Graham, who is also a State representative, said yesterday. She added, however, that the proposals might serve as "models" for statewide tax reform.

The measures that will be sent to the legislature in the form of home rule petitions include:

* A request for permission to hold a referendum this spring to ask city voters if they favor overriding Proposition 2 1/2;

* A request that the city be allowed to levy payroll taxes and taxes on "professional and research" services including consulting; and

* A request that the exemptions granted Harvard, MIT and Lesley under state law be revoked, and those institutions taxed at either half the current tax rate or at the full tax rate.

Each of the requests must be approved by the legislature and signed by Gov. Edward J. King, and then reapproved by the City Council or city voters before taking effect. Without some change in the law or some form of additional revenue, the city's budget will be cut by almost $15 million next year, a reduction that could cost as many as 1000 city workers their jobs.

The council voted not to request permission to levy a 2-per-cent sales tax. "I don't believe we sho ld be creating new taxes to take the place of the old," councilor Kevin Crane '72 said, adding that he favored asking the legislature only for permission to hold an override election and for the power to tax universities and colleges.

Councilor David Sullivan, who urged council members to back the relief requests unanimously, said after the vote that the 6-2 margin "is certainly not going to help" efforts to win concessions from the legislature.

A series of speakers--most representing city employees unions--urged that the council adopt the package.

"We busted our humps trying to defeat Proposition 21/2 in the fall. Now we're asking the city councilors to bust their humps getting us some relief from the state legislature," John Rocca, president of the Cambridge firefighters local, said.

Police union spokesman Joseph Bellissimo added "a city that has come as far as Cambridge cannot go backwards because of 2 1/2. There must be a way to keep people working, to keep the public protected."

Pledging to compaign for new taxes or an override of 2 1/2 in a local referendum, Jerry McDonough, a spokesman for the Cambridge Coalition Against Proposition 2 1/2, said, "these are the tools we need to save the city."

"I hope no city worker loses their job--we've all got to stay united," James Cassidy, president of Local 195, Independent Public Employees Association, the city's largest union, said.