AUGUSTA — Gov. Paul LePage’s bill giving him the power to appoint the state’s top law official is in trouble.

The House of Representatives on Thursday voted 115-32 to reject the proposal, which would strip the Legislature of its ability to choose the attorney general and give it to the governor. The bill faces additional votes in the House and Senate.

The proposal is one of three in which the governor has tried to wrest the Legislature’s authority to elect the state’s constitutional officers.

Currently the attorney general, secretary of state and the state treasurer are elected by the Legislature. LePage has proposed making the attorney general and treasurer gubernatorial appointments. Another bill would eliminate the secretary of state and install a lieutenant governor, who would be popularly elected on the same ticket as the governor.

Critics have described the proposals as power-grabs. The vote on the bill to appoint the attorney general suggests that Republicans and Democrats are uncomfortable with the changes.

Rep. Roland Martin, D-Sinclair, said during the brief floor debate that the proposal is “ill-conceived and irresponsible.”

Hank Fenton, the governor’s deputy legal counsel, said during the public hearing that the proposals would make government more efficient because the three officials would report to “one central boss.”

Maine is the only state in which the Legislature elects its top law official, according to the National Association of Attorneys General. Forty-three states and the District of Columbia popularly elect their attorneys general, and the position is appointed by the governor in five states. In Tennessee, the state supreme court fills the position.

All three bills face long odds in the Legislature, which is divided by a Republican-controlled Senate and a Democratic-controlled House of Representatives. Also, all three proposals require altering the Maine Constitution, which means two-thirds of the Legislature must approve the measures before each is sent to voters for final ratification.