ST. PAUL — A judge is considering how to deal with a dispute over whether Republican Michelle Fischbach can serve as both Minnesota’s lieutenant governor and as a state senator.

The dispute arises from Democratic Gov. Mark Dayton’s decision to appoint Lt. Gov. Tina Smith to the U.S. Senate last month. Under the Minnesota Constitution, Fischbach, as president of the state Senate, became lieutenant governor.

But she refuses to resign her Senate seat. The narrow GOP majority in the Senate could hang in the balance.

Attorney Charlie Nauen argued before Ramsey County Chief Judge John Guthmann on Tuesday that Fischbach can’t serve in both branches.

Fischbach’s attorney, Kevin Magnuson, argued that the court shouldn’t be deciding who can be a state senator.

Minnesota Public Radio reports the judge didn’t say when he’ll rule.