A domestic short-haired cat — dubbed Dempsey because of his fighting spirit — is in the care of a veterinarian after being shot and apparently run over by a car in Mashpee.

MASHPEE — A domestic short-haired cat — dubbed Dempsey because of his fighting spirit — is in the care of a veterinarian after being shot and apparently run over by a car in Mashpee.

Mashpee police are investigating the incident as a case of animal cruelty, according to Police Chief Scott Carline.

Sylvia Ferguson, of West Yarmouth, was on her way to her mother’s house in Mashpee on Tuesday when she saw a cat that looked injured meowing loudly on the side of the road near Otis Trailer Village.

“I sat on the ground next to him and he sat on my lap,” she said. “He was hurt, meowing, looking for help. The eye was messed up and there was a gaping hole in his leg.”

Photo gallery: Dempsey is treated at a local animal hospital

She took the cat to her mother’s house and fed him tuna before bringing him to an animal-loving neighbor, who got in touch with the Centerville-based New England Society for Abandoned Animals.

The agency took the cat to a Mid-Cape veterinary clinic that treats “critical” rescued animals, said Deborah Doe, society president. The clinic has requested its name not be used.

The veterinarian there determined that Dempsey had been hit twice with what resembled birdshot, once in the back and once in the knee. He also had signs of being hit by a car.

“He’s a fighter,” said Doe, who added that the cat was named after Jack Dempsey because of his fighting spirit and his resemblance to the boxer.

Because of an upper respiratory infection, Dempsey is on antibiotics and will not be able to have surgery to remove the pellets until the infection heals, Doe said. Dempsey also may need to have his left eye removed; the veterinarian said it was unclear what caused the eye injury. Dempsey is malnourished and has not been neutered, according to Doe, but she said he likely had a home at some point because he is gentler than most feral cats.

His tattered ears, however, suggest “he has been out there for some time on his own,” Doe said. The veterinarian estimated he is 6 years old.

On Thursday, Dempsey seemed in good spirits, purring as he walked around his cage, despite being in isolation while he undergoes treatment.

The society is offering a $500 reward, through an anonymous donor, to whomever helps find Dempsey’s attacker and is asking anyone with information to call 508-771-7800 or write to P.O. Box 1041, Osterville, MA 02655. The agency is at 89 S. Main St., Unit A-1, in Centerville.

The organization, which has six part-time staff members and relies solely on donations, has been in operation since 2006.

Doe said agency representatives met with the Mashpee animal control officer Thursday afternoon to pass on details.

— Follow Sam Mintz on Twitter: @SMintzcct.

Visit the New England Society for Abandoned Animals on the web at www.nesaa.org.