When Gov. Kristi Noem of South Dakota showcased her new teeth in a sleekly produced video posted to social media on Tuesday, it seemed like a baffling move: to advertise that she, the head of one state, had flown to another for a cosmetic procedure that was documented in detail for her followers.

Now, Ms. Noem has more to chew on.

A nonpartisan consumer group filed a lawsuit on Wednesday against Ms. Noem in Superior Court in Washington, D.C., claiming the social media post was an undisclosed advertisement for the cosmetic dentistry practice in Houston that is featured prominently in the nearly 5-minute post — a violation of the district’s consumer protection law, which prohibits deceptive business practices.

Ms. Noem — a Republican who is reportedly on former President Donald J. Trump’s shortlist to be his running mate — is also under scrutiny in her home state over the dental procedure. On Wednesday, a state senator in South Dakota called for the State Legislature’s operations and audit committee to examine her trip to Texas, particularly whether she used public funds or a state airplane.

A representative for Ms. Noem did not immediately respond to a request for comment.

Smile Texas, the practice Ms. Noem mentions at length in the video, advertises itself as a destination for cosmetic procedures, offering guidance on travel and financing on its website. A representative reached at the company’s main line on Thursday said: “I ran to the phone and I’m not going to talk to you. That’s HIPAA policy. You’re smart enough to know that.”

(HIPAA — the Health Insurance Portability and Accountability Act — governs the use and disclosure of certain sensitive health information. It’s often used — at times incorrectly — as shorthand for “medical privacy.”)

In Tuesday’s video, Ms. Noem, 52, describes how she flew to Houston so “the team at Smile Texas” could fix her teeth, which she said were knocked out in a biking accident years ago. Her testimonial is interspersed with footage of a dentist in the practice and tight shots of her mouth, and it ends with the logo for Smile Texas. Ms. Noem did not include a “sponsored” tag or otherwise label the content.