LSU Alumni Association President Charlie Roberts has no intention of resigning in the wake of what he calls “scurrilous” allegations that he gave a woman a job so she would continue a sexual relationship with him and then paid her some $3,000 a month in hush money after she resigned, Roberts’ attorney said Thursday.

The woman, Kay Heath, countered in a written statement released Thurdsay that she has proof of the monthly checks — “payments made to save his job at the expense of mine” — from December 2012 until this month.

“In time, you will find that all that I claim in my lawsuit is true,” Heath stated, referring to the suit she filed Aug. 1 against Roberts and the Alumni Association. “Only an open investigation with the full cooperation of the Association will reveal the complete truth.”

Roberts, of Baton Rouge, stood by his guns in a statement issued Wednesday through his attorney, Mary Olive Pierson.

“We are confident that I will be exonerated at the conclusion of the matter and the case will be dismissed at the cost of the plaintiff,” he stated.

LSU Chancellor F. King Alexander said Wednesday that the university takes Heath’s accusations seriously and pledged that the school will investigate the matter and “do the right thing by our alumni and our university.”

Roberts noted he has met with or spoken to numerous officials with the Alumni Association since last week.

“I invite and will cooperate with any investigation into the allegations by the Association or LSU,” he said.

Pierson said Thursday that Roberts has no plans to resign.

“He hasn’t been asked to, and he doesn’t have any intention to,” she said.

Heath claims she was involved in a sexual relationship with Roberts while she was married and before going to work for the association. She says she was unable to obtain a divorce due to economic dependence on her then-husband.

“In order to establish her economic independence from her then husband and to entice (her) to continue the sexual relationship, Roberts, on behalf of the Association, offered (her) employment, which she accepted,” states the suit, filed in the 19th Judicial District Court in Baton Rouge. It has been assigned to state District Judge Mike Caldwell.

The alleged sexual relationship and employment relationship continued for a “significant period of time” until April 2012, when Roberts told Heath their sexual relationship was prohibited by association rules and regulations, that certain members of the association’s board had learned of the forbidden relationship and that one of the two would have to resign, the suit claims.

“Roberts informed (her) that, considering his position was far more significant and his salary was many times larger than (hers), (she) should resign,” the suit says.

Roberts, who also is chief executive officer of the association, has an annual base salary of more than $300,000.

Heath alleges in her suit that she was to receive about six months of severance pay worth $21,000 and that Roberts offered her payments of $3,200 a month for the rest of her life. She says she sued Roberts and the association when the payments ceased last month.

Pierson called that allegation “fanciful” Thursday and said she’s never heard of a wage agreement with a former employer that lasts “till death do us part.”

“The allegations of an agreement to pay the plaintiff beyond the settlement she reached with her employer are all false,” Roberts said in his statement. “The allegations of a breach of the nonexistent agreement to pay her beyond the settlement she voluntarily entered are all false.”

Heath maintains she has the proof.

“Payments made every single month in the first week of each month. Payments that began as soon as the lump payment from the Association was exhausted and continued until this month,” she said in her statement. “If this sounds like payments made pursuant to an agreement, it is because that is exactly the case.”

Roberts contends he was blindsided by Heath’s accusations when he was first contacted July 30 by her attorney, who demanded that Roberts pay $192,000 to Heath to avoid the filing of the suit.

“Needless to say, I did not agree, nor did I pay the outrageous demand,” he said.

LSU is run separate and apart from the Alumni Association, which is a 501(c)3 nonprofit. The association reported total revenue of $7.3 million in 2011 and $4.2 million in 2012, according to an association filing with the IRS.