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The Connecticut Republican Party is claiming that East Granby resident Tami Zawistowski’s victory over Peter Hill in the 61st House District race was a referendum on Democratic Gov. Dannel P. Malloy.

The special election held Friday showed that Zawistowski defeated Hill by more than 540 votes. Zawistowski will fill the seat previously held by the late Elaine O’Brien of Suffield. The district includes East Granby, Suffield, and part of Windsor.

“Tonight’s results are also a clear referendum on the failed economic policies of Dan Malloy which have given us the worst economy in the nation, brutally high taxes, and an unemployment rate that continues to far exceed the national average,” Republican Party Chairman Jerry Labriola Jr. said.

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A spokeswoman for the Democratic Party said that the Republican Party’s perspective on the race is not accurate.

“I commend Peter Hill on a hard fought race and congratulate Tami Zawistowski. But please, someone give Jerry Labriola a reality check,” Sandra Lyons said. “We realize his party is in shambles with their recent party leader being indicted in addition to their leading candidate for governor being fined for violating election law. As much as Jerry needs good news, a special election for a state house race is not an indicator of anything for November.”

Zawistowski, who runs Resource Books LLC, a company that deals in rare and used books, ran and lost in 2012 to O’Brien, a popular town clerk in Suffield. O’Brien died in February from cancer.

Hill was a political newcomer who had served on the Suffield Police Commission.

Zawistowski’s victory brings the number of Republican lawmakers in the House up to 54. It’s the second special election Republicans have won since Rep. Sam Belsito picked up a seat in the 53rd District representing Tolland, Ashford, and Willington.