When Crystal Marie Garcia decided to try the home-rental service Airbnb for the first time, she had a few questions.

Ms. Garcia, who is from El Paso, was planning a May trip with her family to the Chicago area and wanted to know if the places she was considering could accommodate her needs as someone with muscular dystrophy. Unfortunately, she said, her questions appeared to scare off at least two potential hosts.

She said she feels that if she had not mentioned her disability, “they would have rented to me, no issue.”

Ms. Garcia is not alone in feeling that way. Other users have reported similar bias, and a new Rutgers University study — based on more than 3,800 Airbnb lodging requests sent by the researchers — suggests it may be common: Travelers with disabilities are more likely to be rejected and less likely to receive preapproval, or temporary clearance, for a potential stay, the authors found.