The Texas Senate is not investigating a sexual harassment complaint against State Sen. Charles Schwertner, though the Senate earlier this summer changed its sexual harassment policies to give senators the ability to launch such investigations.

Lt. Gov. Dan Patrick said he is “deeply concerned” about the “serious allegations” against Schwertner, R-Georgetown. But the Senate is waiting first for the University of Texas to conduct its own investigation.

“The Texas Senate is awaiting the conclusion of the investigation and expects a full report on this matter,” Patrick said in a statement to the media.

Other members say the Senate needs to be more aggressive.

“I will repeat the call I made in December and ask the Texas Senate to investigate any allegations of sexual harassment, discrimination, abuse or bullying by Senators or Senate staff," said State Sen. Sylvia Garcia, D-Houston.

On Tuesday, the Austin American-Statesman reported that Schwertner has been accused of sending explicit images and texts to a graduate student on campus who was seeking career advice. Schwertner has denied any improriety, and on Wednesday released a statement through his attorneys.

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“Senator Schwertner did not send any inappropriate texts as alleged. Period,” it said. “The Senator is devastated over these allegations and is concerned for the unnamed victim. We are in contact with the University of Texas to resolve this matter. Our statements regarding the Senator will be proven in the days and weeks to come. Until then, Senator Schwertner deserves the courtesy of holding judgment until he is afforded the opportunity for a fair process to occur.”

In May, the Senate instituted a new sexual harassment policy that applies to “all senators, senate employees … and the Office of the Lieutenant Governor.” The policy doesn’t require the Senate to investigate accusations of sexual misconduct, but it was changed to allow the Senate to order investigations of its members.

The old policy, adopted in 1995, stated that staffers were subject to investigations if accused of sexual harassment but was not clear as to whether the Senate could initiate investigations of members. No sexual harassment complaints have been filed in the Texas Senate since 2001.

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“The revisions address everyone who routinely works in the Capitol including unpaid interns, and provide a clear definition of the types of behavior that could constitute sexual harassment,” State Sen. Lois Kolkhorst, a Brenham Republican, wrote in a letter to her colleagues in late May.

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Schwertner met the unnamed graduate student on the UT campus event in the summer, according to the American-Statesman’s report. After they exchanged messages on the social media site Linkedin, they began texting one another. The Statesman reported that during an exchange on career advice, Schwertner wrote that he “just really” wanted to have sex with the woman, and sent her what appeared to be a picture of his genitals.

The student then complained to the school, which is investigating the matter.

Patrick on Wednesday questioned how details of the investigation had been leaked to the media.

“I was also concerned yesterday to see that numerous University of Texas officials spoke to the media, potentially jeopardizing the integrity of a serious investigation,” Patrick said on Wednesday. “I am calling on the university to complete their inquiry in a professional manner, protecting the privacy rights of both parties.”

University officials declined to comment Wednesday, saying they could not confirm whether there is even an investigation underway.

Schwertner is the third member of the Senate to face accusations of sexual misconduct. In December, State Sens Borris Miles, D-Houston, and Carlos Uresti, D-Helotes, denied media reports that accused them of inappropriate behavior.

Uresti resigned from the Senate this summer after being found guilty in February by a federal jury on 11 felony charges in connection with his involvement in a now-defunct San Antonio oilfield services company that defrauded investors. His resignation was not related to the claims first reported in The Daily Beast.

Schwertner, a doctor first elected in 2012, is running for re-election in November against Round Rock Democrat Meg Walsh. Schwertner, who is married and has three children, is the chairman of the Senate’s Committee on Health and Human Services.

But Republican leaders in the Texas Senate said they will wait until UT finishes its work.

“As a member of the Texas Senate, due to the serious nature of this allegation, I am awaiting the full investigative report on this matter from the University of Texas to be released to the public,” said State Sen. Paul Bettencourt, R-Houston.