Italians began going to the polls today to vote in nationwide local elections that party leaders here have turned into a major test of strength for the five-party coalition led by Socialist Prime Minister Bettino Craxi and for the coalition's major adversary, the Communist Party.

Although the campaign that closed Friday has been seen generally as one of the most lackluster in recent Italian history, with television ads and handbills replacing the emotional mass rallies of the past, top politicians here have sought to convince voters that the election is of historic importance.

Most attention has been focused on speculation as to whether the powerful Communists will duplicate their performance in last year's European Parliament elections, when with 33.3 percent of the vote they narrowly outpolled the Christian Democrats for the first time in Italian history.

Today 44.5 million Italians began voting in a two-day election to choose new local councils in 15 of Italy's 20 regions, 86 of its 95 provinces, and more than 6,000 of its 8,090 towns and cities.

The outcome of the vote will have no direct effect on the composition of the national parliament, elected in 1983 and not scheduled for a new vote until 1988. But it is likely to have a psychological and political impact on the status of the current government, and relatively little attention has been paid to local issues.