Residents of Climax told Kalamazoo County Sheriff's officials that the incidents appear to have started in March and continued into September.
A squirrel also was found with duct tape wrapped around its face, Undersheriff Pali Matyas said.
Climax is about 50 miles southeast of Grand Rapids.
"We have mostly cats who have been tortured and abused," Matyas said. "Some have been killed. Some have been beaten quite badly."
Cat owners who took their pet to a veterinarian were told the animal suffered a blunt-force type of beating.
The dead or injured cats have been found in a front yard, in the village cemetery and other locations, he added.
A group of juveniles has been identified as persons of interest in the beatings and killings.
"We have a big concern any time you're torturing animals because that's just very bad and strange behavior," Matyas said. "What worries us is what occurs when they kick it up a notch? Are they going to start hurting people? We want to nip it in the bud."
A police investigation was started last week after the Sheriff's Department was told by residents about the incidents.
"One of the problems we're running into is that a lot of people are talking about it, but not a lot of people were picking up the phone to call the sheriff's office," Matyas said.