On March 14, 2013, Gonzalez was arrested and charged with driving while intoxicated. According to police, Gonzalez was in a car accident at 2 a.m. with one car and a bicycle. On March 18, 2013, Gonzalez apologized during a speech on the House floor. "I want to be clear about this: I made a mistake and I am deeply, deeply sorry for it. I am sorry for the shame I have brought upon this House and my district," she said. Following her speech, legislators applauded and gave her a standing ovation. Gonazlez reportedly had a blood-alcohol level of twice the legal limit. The magazine Texas Monthly named Gonzalez one of the 10 worst legislators in 2013 as a result of her arrest. Sentencing On May 2, 2014, Gonzalez was sentenced to 15 days in jail after pleading no content to the charge.

Gonzalez was one of the eight members of the Committee on Transparency in State Agency Operations when it oversaw the investigation into a possible impeachment of University of Texas Regent Wallace Hall in 2013 and 2014. On August 11, 2014, the transparency committee voted 6-1 to censure Hall as opposed to impeaching him. He was the first regent to have been censured by a committee of the Texas State Legislature. After he was appointed by Gov. Rick Perry (R) in 2011, Hall began looking into what he believed to be clout abuses within the University of Texas system. Hall investigated the university's forgivable-loans program, admissions policies, and preferential treatment to politically-connected individuals. Hall, as an individual citizen and a regent, filed public information requests with the University system. In June 2013, the transparency committee began investigating whether Hall revealed protected information about students and exceeded his role as a regent in requesting large amounts of information. Some supporters of the investigations into Hall, including state Rep. Lyle Larson (R), a member of the transparency committee, argued that Hall's actions were politically motivated. Others, such as University of Texas, Austin Public Information Office attorney Carol Longoria, said that his records requests were unreasonable and may have violated students' privacy. Critics of the proceedings, including Gov. Rick Perry and Hall, argued that legislators' efforts to remove Hall from office were politically motivated and that Hall acted in the best interest of the state in his efforts to investigate potential abuses. Several legislators were named in investigations into possible political favoritism in the University of Texas admissions process. In February 2015, an independent report by Kroll Associates, commissioned by the Regents Board, stated that there was a "pattern of special treatment for well-connected applicants to UT." While the report did not show evidence of any quid pro quo, it said that "extra acceptances were extended every year to accommodate special cases" and that the "President’s Office ordered applicants admitted over the objection of the Admissions Office." In March 2015, the Travis County Grand Jury concluded a six-month investigation into Hall, deciding not to pursue criminal charges against him but recommending that the state remove him from office. The jury stated that Hall's open records request deadlines were unreasonable and that he released confidential student information to the attorney general's office and his lawyer. The state did not remove Hall from office; his term expired in February 2017. Read more about the investigations into Hall's information requests and Hall's investigations into alleged clout abuses here.