The couple rang police in Jönköping, south of Stockholm, after the animal, who had been missing for several days, was found hit by a car.
According to reports in regional newspaper jp.se, the pair asked to escort the cat to a vet, but the police officers who arrived on the scene said that they would take care of the pet instead.
A police document seen by the paper states that one of the officers repeatedly struck the animal with a baton, put it into a bag and then placed it in the couple's freezer. The report explains that the staff member understood that the cat had damaged both of its legs as well as its spine and therefore wanted to act quickly to minimize the pet's pain.
However the couple believe that the animal was still alive when it was put into the freezer, because it appeared to have changed position when they looked at it later.
The owners demanded an autopsy, with the results suggesting that the cause of death for the animal was trauma.
They have now taken their case to Sweden's parliamentary ombudsman, a body which looks into cases in which residents believe they have been unfairly treated by a public authority.
The couple argue that the cat would have survived if it had been treated by a trained vet. They have also requested information on whether the officers were qualified to determine the cat's condition and complained that no ID checks were carried out on the animal, despite the fact that it was tagged with an ear tattoo.