Lawmakers are calling for a truly independent investigation into the sexual harassment claims against Gov. Andrew Cuomo - as he keeps changing who will investigate the allegations.

It comes after a second woman, 25-year-old Charlotte Bennett, from Westchester, says the governor harassed her last spring and asked her personal questions about her sex life.

On Sunday morning, the governor asked former judge Barbara Jones to oversee the investigation. It raised eyebrows because Jones once worked with one of governor's closest advisers.

Cuomo also broke precedent by not handing the case over to state Attorney General Letitia James.

Throughout the weekend, there's been much push back from lawmakers on both sides of the aisle. Several Democratic senators, including Majority Leader Andrea Stewart-Cousins and Kirsten Gillibrand, called for a truly independent investigation.

Dutchess County Executive Republican Marc Molinaro tweeted saying, "certainly the accused, Governor Cuomo - cannot be allowed to select who investigates."

Around 11:30 a.m., James herself responded - saying she needs to be in charge.

James made it clear in a statement, "I stand ready to oversee that investigation and make any appointments necessary. Given state law, this can only be accomplished through an official referral from the governor's office and must include subpoena power."

She then issued a follow-up statement, addressing reports Cuomo's asked New York's top judge, Janet DiFiore, to work with her to investigate the allegations.

James said in part, "To clarify, I do NOT accept the governor's proposal. While I have deep respect for Chief Judge DiFiore, I am the duly elected attorney general and it is my responsibility to carry out this task, per Executive Law."

DiFiore is New York's top judge who was appointed to the position by Cuomo himself.

James, reiterating to Cuomo who was once the attorney general, that by law - she needs to have sole supervision of the case.

That means she can legally call on anyone in the governor's office to testify and ask to see any documents she wants. That's not the case right now, but she will ultimately do what the governor asks.