No public records confirming a Naples incident were available from the Naples Police Department or the Collier County Sheriff’s Department. The agencies said the stores are outside Naples city jurisdiction, and officials noted that the names of people who have not been arrested are not always made public. Alting has not responded to requests for comment about the Florida allegation.

In Indiana, authorities are reviewing several reported incidents. Lafayette police say six alleged shoplifting incidents at the city’s Commerce Drive Walmart in August and September are under review by special prosecutor Vicki Becker of Elkhart County. As of Oct. 20, Becker had not filed charges. Police have not publicly identified Alting as the suspect in those incidents.

Alting was also suspected of shoplifting at the Lafayette store on Sept. 22 and at the Monticello Walmart on Oct. 1, according to people familiar with those investigations. Monticello police had not provided details of the allegations. White County Prosecutor Mark Delgado had not responded to requests for comment.

A Walmart spokesperson said the company is continuing to work with local law enforcement on the investigation.

Alting said in an Oct. 7 statement that he had experienced concerning changes in his judgment and cognitive functioning and was seeking medical evaluation and treatment. He said he had done things that were wrong and out of character, and apologized to his family, constituents and store employees. He has not specified a diagnosis.

Alting also said he would step back from campaigning, although television campaign commercials continued to air. Matt Zapfe, executive director of the Indiana Senate Majority Campaign Committee, said he understood Alting would issue another statement later in the week. Alting is seeking re-election in the 22nd District, where Democrat Natasha Baker is his opponent.

Baker said public service requires honesty, accountability and sound judgment, and that she was saddened by the reports. The allegations remain unresolved, and no charges have been filed.

Lafayette police Sgt. Nathan Stoneking has said thefts at the city’s two Walmart stores are a daily occurrence, sometimes bringing officers to a store several times a day. Police and West Lafayette police Lt. Jon Eager described how store loss-prevention staff may use surveillance footage to document suspected thefts and, in some cases, review archived video for evidence of multiple incidents. The response can vary depending on the circumstances, a person’s prior record and the value of the goods, officers said.