Officers don't know the motivation behind it and Lincolnshire Police told Sky News no official reports have been lodged, but it had been communicated to local officers through "word of mouth".
In a Facebook post, South Holland Police said while the cats did not appear physically harmed, the alleged incidents might have caused the animals distress or anxiety.
Cats in a rural Lincolnshire village have allegedly been returning home with parts of their fur shaved off, police have said in an appeal.
"The cats in question are someone's pet, part of their family, and not only will these actions cause anxiety to the animal they also cause worry to their owners.
In Pinchbeck, Lincolnshire, the claims had been brought to the attention of local officers who appealed for anyone affected to come forward.
