The Connecticut State Senate completed ratification yesterday of a constitutional amendment to give the District voting representation in Congress.

By a vote of 21 to 14, the State Senate approved the amendment that had passed the Connecticut House two weeks ago.

Connecticut is the sixth state to ratify the amendment. Eight states have rejected it. Passage by 38 states is needed for ratification.

"In a democratic society, the worst injustice is that which deprives a citizen of his voting right," said Sen. Steven Casey, a Democrat, in introducing the bill. "In the Capital of the United States, the world's greatest democracy, that very injustice is sustained upon 690,000 citizens."

Currently, Washington has just a delegate in the House of Representatives who can vote only in committee. The amendment would give Washington at least one congressman and two senators, all with the right to vote.

The amendment would give the city a second congressman if the population shows a large enough increase after the 1980 census.

Arguing before the Connecticut Senate yesterday, Casey used familiar arguments in support of the amendment. He said that Washington had a population larger than that of seven states, that residents pay more federal taxes than those in 11 states and that taxation without representation had led to the American Revolution.

There was strong opposition to giving Washington two U.S. senators as well as a voting congressman. Opponents of the amendment said that it would, in effect, give the city the status of a state.

"It's a statehood we want to give them, without the problems and responsibilities of statehood," said Sen. George Gunther, a Republican.