Michigan yesterday became the third state to ratify the D.C. voting rights amendment.

By a vote of 20 to 13, the bare minimum needed for passage, the Michigan Senate approved the amendment that would give the District two senators and one or two House members.

"We had hoped to be the first," said the resolution's sponsor, State Sen. Jackie Vaughan III (D-Detroit). Legislatures in New Jersey and Ohio previously had ratified the proposal.

Vaughn, nowever, "had the privileged" of voting for ratification in both houses of the legislature. He introduced it last September as a member of the House, steered it through committee to the floor and then was elected to the Senate last month, where he voted for it on the floor yesterday.

An aide to Senate Majority Leader William Faust noted that the absence of six members made the outcome so close. He said he believed only one Republican voted for it, even though it had the outspoken support of the popular Republican Gov. William Milliken.

Speaking for the opponents, Sen. Donald Bishop (R-Oakland County), the GOP floor leader, said ratification would give the city of Washington "immense power, unequal to that of any state." Bishop said the way to solve the problem is to retrocede the residential sections of the city to Virginia.

When the resolution passed the Michigan House on Nov. 29, seven Republicans joined 53 Democrats in providing a 60-to 32 margin, four more than was required for passage. The opposition wad made up of 22 Republicans and 10 Democrats.

A staff memo circulated to Republicans in the Michigan House on Sept. 8 said "any Republican who is seeking black support or who is dependent upon black support must certainly support the amendment."

Kalmain D. Smith, director of the GOP's program and research section, went on to advise Republicans to "send this potential hot potato on its way before the public and media become sufficiently aware of its existence to turn it into a major issue, as ERA has become."

That memo prompted the American Legislative Exchange Council, which is leading the nationwide opposition to ratification, to brand the planned speedy action as racist.