Voters turned out in droves yesterday in New Jersey and Arizona, two states where the Democratic primary contest is tight, but many forgot one key detail: registering to vote.

In New Jersey, poll officials said they saw an unusually large number of would-be voters who had either failed to register with a political party at all or wanted to vote for a candidate from a different party (only registered party members may vote in primaries in the Garden State). Blame it on the earlier-than-usual primary, which was moved to February from June. Similar confusion arose in California, where independent voters are allowed to vote in the Democratic contest but not on the Republican side.

Traditionally, New Jersey primaries attracted relatively few voters, because the presidential nominees were nearly always already decided. This year’s race was a stark contrast, drawing a flood of voters, many of whom had never participated in a primary, according to election officials and observers.

“We’re seeing unaffiliated voters trying to vote, and others who can’t remember what party they registered with,” one GOP official monitoring the polls said. “One lady said she thought she had been a Republican for 10 years, but she had never actually changed her registration.”

Governor Corzine, a Democrat, had planned to cast his vote at 6:15 a.m. at his regular polling place in Hoboken, N.J., but had to wait after two voting machines malfunctioned. About a dozen voters were turned away before the machines were fixed, election officials said. Mr. Corzine, who has endorsed Senator Clinton, a Democrat of New York, for president, cast his vote shortly before 7 a.m.

In Arizona, confusion over voter registration also meant that some voters arrived to cast ballots, only to be told their vote would not count or to be turned away.

The glitch occurred because Arizona’s independent voters mistakenly believed that since they are allowed to vote for Democrats or Republicans in other elections, they could do so in presidential primaries. But by state law, the vote yesterday was open only to registered party members.

[In Connecticut, what was expected to be a record voter turnout had local poll workers scrambling to keep up with demand, the Associated Press reported.

Several towns had to photocopy ballots, while officials in Stratford put a call out to the town’s printer to order new ballots long before the polls closed at 8 p.m.

Secretary of the State Susan Bysiewicz predicted that turnout would far exceed the record 43.3% turnout for the closely watched 2006 Senate Democratic match-up between Senator Lieberman and Ned Lamont.

“Turnout was very strong,” she said. “We think we are well over 50% statewide and that is very exciting.”

Democrats were choosing between senators Clinton and Obama, while Republicans handed Senator McCain a wide-margin win over Mitt Romney.

Democrats in Manchester flooded the polls, prompting town officials to copy 3,000 additional ballots.