During a November 10, 2010, hearing of Fiscal Review Committee, Todd asked administrators if the CoverKids program verified the immigration status of women receiving prenatal care. When told that the program did not do so and that it would be illegal to do so under federal law, he said, "They can go out there like rats and multiply then, I guess." His comment, footage of which is available here, was widely condemned, and he clarified his remarks with the Associated Press, saying that he was wrong and should have used the words "anchor babies."

Todd was arrested on October 11, 2011, for driving under the influence of alcohol. He also faced gun charges for having a loaded handgun in the car while under the influence. He took a field sobriety test but refused to submit to a breathalyzer test. Todd was the sponsor of a bill to allow people who are not drinking to carry guns in establishments which serve alcohol. After being charged, Todd gave up his chairmanship of the State and Local Government Committee. On January 18, 2013, he pleaded guilty to DUI and possessing a gun while under the influence. He was sentenced to two days in jail (minus the eight hours he was in jail after his arrest), a $35 fine, 24 hours of community service, and a year of probation without the right to carry a gun. As part of the plea bargain, he was also required to install an alcohol-monitoring ignition interlock device on his car, take an alcohol safety course, and participate in a Mothers Against Drunk Driving victims-impact panel. Reading a prepared statement to the press, Todd said, "I want everyone to know that this incident was not the result of excessive drinking but instead it was the result of taking prescription medication and later consuming less than two glasses of wine over several hours. But the mixture resulted in an unknown effect and the ultimate mistake of me driving. I clearly recognize that I made that mistake. I cannot change the past. The events of Oct. 12, 2011 (the stop occurred late on the night of Oct. 11) and today will stay with me for the rest of my life."

The Tennessean reported on March 1, 2013, that Todd had lived in a Nashville house owned by his lobbyist friend Chuck Welch for part of 2011 without paying rent. Todd confirmed that he had stayed at the house multiple times in 2011 but did not give any details of the length or dates of his stays. Although Welch and his lobbying firm Farris, Mathews and Bobango lobbied for bills before the State and Local Government Committee, which was chaired by Todd until October 2011, Todd told reporters that his connection with Welch "has not affected my independent judgment as a lawmaker.” These actions were legal because of an exception to Tennessee's ban on legislators receiving gifts from lobbyists in the case of long-time friends. Additionally, it was not illegal for Todd to reside outside of his district because the residency requirement only applied on the general election day, not during a legislator's term of office.