Her mother confronted the suspect, who fled on foot. Both later identified the voyeur as a white man wearing a dress and a blond wig, according to the document. Another witness reported seeing the suspect leave in a vehicle that was later discovered to be registered to Ms. Smith.

Ms. Smith’s roommate confirmed to the police that she is, indeed, a transgender woman and identified clothes worn by the suspect in surveillance footage as belonging to Ms. Smith, according to the document, posted online earlier by EastIdahoNews.com and obtained separately by The New York Times.

According to the document, an affidavit of probable cause for warrantless arrest, Ms. Smith told a detective that she had made videos in the past of women undressing for the “same reason men go online to look at pornography” and allowed the detective to unlock the iPhone.

Ms. Smith is represented by a public defender.

Target, which has 1,792 stores nationwide, said in a statement that it was committed to creating “a safe and secure shopping environment” and that it immediately cooperated with local law enforcement as soon as it learned of the case.

The retailer has been the subject of a boycott petition created by the American Family Association, which contends the transgender fitting room and bathroom policy would give sexual predators access to victims. The petition has collected nearly 1.4 million signatures since April, according to the group’s website.