Secretary of State Tom Schelder, currently facing sexual harassment allegations, speaks during a press conference, Wednesday, March 14, 2018, at his office in Baton Rouge, La.

The allegations against Secretary of State Tom Schedler hung over a Senate committee hearing on Wednesday like a dark cloud on the verge of bursting into rain.

For 30 minutes Schedler and his assistants fielded questions from the Senate and Governmental Affairs Committee about the day-to-day workings of the Secretary of State's office — normally an innocuous process that agencies go through every four years.

Then, for the next seven minutes, Schedler sat mostly quiet as his top aides discussed the office's sexual harassment policies and what the agency could do — will do — to make them better.

"Do you think there are any revisions needed to the policy?" Committee Chair Karen Carter Peterson, D-New Orleans, asked Human Resources director Ashley Gautreaux, sitting to Schedler's left.

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Turning to another of Schedler's top aides Kyle Ardoin, seated to the secretary's right, Peterson asked: "What do you think, as the first assistant, needs to be revised in the sexual harassment policy at the Secretary of State's office?"

Never directly mentioned but constantly on the verge of bursting to the forefront: An employee in the Secretary of State's office has filed a lawsuit claiming Schedler harassed her for more than a decade, sending her love letters and sex tapes then retaliating when she refused to go along with his repeated sexual propositions.

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Schedler has said he had a "consensual sexual relationship" with the woman in the past — a claim that the woman denies.

The lawsuit is ongoing and has been much discussed within the State Capitol, as Schedler is the highest-profile public servant in Louisiana to have been recently accused of harassment amid a national evaluation of sexual misconduct issues and the #MeToo movement.

The Secretary of State's office acknowledged during the hearing that it is looking to enhance its policies, as lawmakers consider a law that would apply to all state agencies. Schedler, who has said he will not step down despite calls for his resignation from Gov. John Bel Edwards and others, even offered his own advice at one point during during the discussion Wednesday.

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"There should be a consistent harassment policy across all agencies," he said. "I agree with that 100 percent — it shouldn't be addressed by agency. It should start right here, and it should be something consistent."

Schedler did not elaborate on what he thinks such a policy should entail, though his office promised to get specific list of ideas back to Peterson soon.

Lawmakers have embraced legislation this session that aims to discourage sexual harassment in state government and define how harassment claims are handled. A final bill, which is still being fine-tuned, will next come up on the Senate floor.

As Peterson peppered the Secretary of State's office with questions about harassment policies and what the agency can do to improve, she only vaguely alluded to the lawsuit that Schedler faces.

"There's a lot going on and we don't have to tap dance. I'm asking you, forget the legislation and whether it passes or not, will you be implementing anything different in your current policies which have not been revised since 2013 with regard to sexual harassment considering climate and circumstances?" she asked Ardoin as Schedler sat silently.

Peterson then continued her questioning in a back-and-forth that could come across as code if everyone in the room wasn't already aware if the allegations.

"Notwithstanding anything of current nature there, that's not going to stand in the way of us, we, this department doing our job," Schedler said.

"I'm asking you because we're recreating the department right now, what are the improvements you can make?" a stone-faced Peterson said. "This is a fair question in your department with respect to sexual harassment."

Schedler promised his office would return with more specifics "by the week's end."

"I will remain out of that process, OK," Schedler said. "I'm not going to want to put (employees) on the spot."

"I really don't care if you're in it or not, you run the agency," Peterson said.

Follow Elizabeth Crisp on Twitter, @elizabethcrisp.