BOSTON — Republicans hoping to loosen the Democratic party’s tight grip on state government quickly pounced on guilty verdicts against three former state probation officials, saying the case pointed to the consequences of one-party domination in Massachusetts.

A federal jury on Thursday convicted former probation commissioner John O’Brien and two deputies of scheming to rig the agency’s hiring process to favor job applicants referred by powerful state lawmakers over more qualified candidates. Attorneys for all three are promising appeals.

No legislators were charged in the case. But Kirsten Hughes, chairwoman of the state GOP, urged voters to react to the verdict by electing new leaders in November.

“What kind of rotten atmosphere exists on Beacon Hill that forced public employees to break federal law and commit conspiracy and wire fraud in order to appease a Legislature dominated by Democrats in exchange for budget increases?” Hughes asked in a statement.

Democrats currently control all statewide offices, the state’s entire congressional delegation and hold overwhelming majorities in both branches of the Legislature.

The verdict was “proof positive that the last eight years of one-party rule has bred corruption and waste in state government,” said Republican candidate for governor Charlie Baker.

House Speaker Robert DeLeo and Senate President Therese Murray both issued statements repeating past assertions that they had done nothing wrong.

Democratic Gov. Deval Patrick, who is not seeking re-election, said Friday that he expected the verdicts to end the criminal aspect of the case and noted that he signed legislation in 2011 to overhaul probation hiring procedures after reports of abuse first surfaced.

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