Virginia’s evenly split Senate had its first tie vote of the session Tuesday, on a bill related to union elections that Lt. Gov. Bill Bolling (R) was powerless to weigh in on.

The Senate voted 20-20 on a measure proposed by Sen. Bryce Reeves (R-Spotsylvania) that called for amending the state’s constitution to guarantee voter privacy in union elections.

The bill died with the tie vote, with every Republican voting in favor and every Democrat against. Bolling, who presides over the Senate, can break tie votes, but he is not allowed to weigh in on constitutional amendments.

Held over from the 2012 General Assembly session, the bill cleared the Senate’s Privileges and Elections Committee between sessions and came to the Senate floor Tuesday. The legislation came as Republicans in other states, including the longtime labor stronghold of Michigan, push to rein in unions.

Reeves said the amendment was needed to thwart federal legislation known as “card check,” which he said would deny workers their right to secret ballots in union elections.

“The amendment will protect the rights of all Virginia workers,” Reeves said.

Union officials opposed Reeves’s measure, saying that it would allow employers to stall the organizing process and intimidate workers who support the creation of unions. Sen. Richard L. Saslaw (D-Fairfax) said it wasn’t needed because the federal legislation had gone nowhere in Washington.

“There is absolutely no chance this would ever pass there or here,” Saslaw said.