A city-wide referendum that would have allowed Cambridge to establish a municipal cable television company has failed by 38 votes after a recount of last month's ballots. Cambridge officials announced yesterday.

When the ballots were counted after the November 8 election the proposition was thought passed by 102 votes, but officials of the Committee for Risk-Free Quality Cable TV, the local group coordinating opposition to the referendum, filed for a recount.

Election commissioners attributed the change to an "error in transcription," Sandra Schier, the chairman of the count, said yesterday. The figures for yes votes and no votes on one tally sheet were reversed when they were transferred to the official tally sheet, she explained.

Kevin Crane, chairman of the committee, said yesterday he was happy with the change. "As the great philosopher Yogi Berra would say, it's not over until it's over," Crane said.

But it may still not be over. Although no further counts are legally possible, referendum supporters watching the recounting process found about 38 ballots which might be invalid, Bruce Berman, consultant to the pro-referendum Committee for Quality Cable, said yesterday.

Berman explained that his group has 30 days to contest the ballots in court. Because of the proportional representation voting system used in Cambridge, the city uses paper ballots in its elections, and through either error or ignorance, some of these are filled out incorrectly.

In one case, Berman said, a voter had written the word "yes" in the box on the ballot reserved for a negative vote, instead of marking an "x" for either yes or no. Election commissioners counted the ballot as a vote against the referendum, a decision which would be challenged if the case goes to court.

Berman said the Committee for Quality Cable has not yet decided whether or not to take court action.

The recount will not change results of any other referendum or election on last month's ballot. The cable TV question was the only close vote and none of the other elections have been contested.

The referendum in question did not ask voters to choose between municipal and private ownership of cable TV, but would have been a step in the state-regulated process of setting up a non-profit city-owned company to allow Cambridge to compete with private companies for the city's cable markets.

Under the proposal, City Manager Robert W. Healy would review all the bids, municipal and private, and would award the city-franchise to the company giving the best offer.

"Cambridge as a city has very high standards," Rosemary White, co-chairman of the Committee for Quality Cable said yesterday. "A city bid, because it offers competition, will force the cable companies to give the best deal possible," she added.

But opponents of the referendum say the city would be biased in favor of its own offer, especially in light of the $250,000 cost of filing a bid. Also, they say, a municipal bid would scare away prospective private companies.

At issue is the potentially lucrative cable market in Cambridge. About 43 percent of the city is college-educated, with an average income of $18,536. Preliminary studies indicate that even if only half of the households in the city subscribe, a conservative estimate, the system will be worth between $25 and $32 million in 15 years.

Because of the high predicted profits, the pre-election campaigning budgets were high.

The Committee for Quality Cable raised about $35 000, mostly from private donations. White said The' anti-referendum groups however, were working with almost $45 000 which was supplied primarily by the New England Cable Television Association, White added.

Schier said that it is not unusual to have a account request especially when a measure passes by a small margin. When the results are as close as 102 ballots, anybody would ask for a recount," she said. The had recount in the city was during the 1980 race for a seat on the Democratic Ward Committee, Schier added.

Cambridge voters cast 29,968 ballots in the election.

Even if the ballots are not challenged and the outcome remains the same, the Committee for Quality Cable will not give up it campaign. Berman said "We will continue to work for the best cable system in Cambridge, making sure that the city puts out the best request for bids and then chooses the one most beneficial to the city," he added