Voters in Hartford, Watertown, and Woodbury filled two vacant Connecticut state House seats in April 25 special elections.
Polletta won with 79% of the vote, defeating Democrat Louis Esposito.
The 68th District includes all of Watertown and part of Woodbury.
In Hartford, former state Democratic Party treasurer Josh Hall won the 7th District seat vacated earlier this year when Democrat incumbent Doug McCrory was elected to the state Senate in a special election.
Hall, a union representative, ran as a Working Families Party candidate after losing the Democratic Party's endorsement to Rickey Pinckney.
Voter turnout was light in Hartford, with just 16% of registered voters casting ballots.
Hall won with 625 votes, Pinckney received 512 votes, and petitioning candidate Kenneth Greene had 367 votes.
Democrats will retain a slim 79-72 margin in the House, with Hall saying he will join the Democratic caucus.
The Senate is tied 18-18.