Long Island lawmakers introduced legislation to reform parts of Gov. Andrew M. Cuomo’s LIPA Reform Act, seeking to fortify the oversight and approval powers of the LIPA board, the state comptroller and the Department of Public Service.

The legislation, introduced May 12 by Sen. Kenneth LaValle (R-Port Jefferson) and Assemb. Fred Thiele Jr. (I-Sag Harbor), also addresses a laundry list of complaints about the Long Island Power Authority, including its rising debt load, the rate-making process and access to cheap hydroelectric energy sources.

The legislation would check LIPA’s borrowing by requiring a public referendum on Long Island for the issuance of new debt. It also would replace an appointed board with an elected board (except for the governor-appointed chairman) and remove a provision from state law that prevents LIPA from buying cheap hydroelectricity from the New York Power Authority.

The bill also would remove a prohibition in current law that prevents local municipalities from forming their own electric utilities.

“LIPA would be responsible to Long Islanders, not Albany,” Thiele said in a statement.

Since the LIPA Reform Act of 2013, LaValle said, “We’ve learned that we need to go further to ensure that we represent an overburdened ratepayer.”

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LIPA declined to comment. A spokeswoman for Cuomo said, “We are reviewing the bill.”

Most measures of the bill would increase or restore oversight at LIPA. The LIPA Reform Act gave the state Department of Public Service only review and recommend authority over LIPA, but the Public Service Commission has no formal jurisdiction, unlike the shareholder-owned utilities in the state.

“We’re delighted,” said Shelly Sackstein, chairman of business group Action Long Island, who has pushed for the reforms for three years. “We’ll do what we can to get it passed.”

The bill also would restore the state comptroller and attorney general’s roles in reviewing contracts. The Reform Act removed the comptroller’s office from reviewing PSEG contracts for LIPA, though it still reviews LIPA contracts. The state DPS also would have to formally approve rate requests, not merely review and recommend them. The bill would address a criticism that arose last year when the LIPA board was considering the three-year $287.4 million rate hike. According to language in the act, the LIPA board could only reject a rate hike if it found an “inconsistency,” in three narrow parameters. Three board members, all legislative appointees, said they found the language restrictive and voted not to pass the increase.

The new language would give the board “full discretion to consider a rate increase, including consideration of the economic impact on ratepayers and the region, after public hearings,” Thiele’s statement said.