The Case of the Cat’s Meow by Crosby Bonsall, 1965.

Four neighborhood friends, who call themselves by the nicknames Wizard, Skinny, Tubby, and Snitch, have their own private detective club.  Their club meets in a backyard clubhouse.  One day, Snitch gives them a case when he becomes worried that someone might try to steal his cat, Mildred.  The other boys think that’s unlikely because Mildred is noisy, and the other boys don’t think that she’s that great, but Snitch loves her and is worried.  The boys decide to keep her in their clubhouse with a special booby trap rigged up in case anyone tries to abduct her.

However, the next day, Mildred disappears.  Snitch is convinced that someone stole her, although the others don’t believe it.  The boys start asking around the neighborhood to find out if anyone has seen her.  When that doesn’t work, they try putting food out for Mildred, but they end up with every cat in the neighborhood except Mildred.

Eventually, they realize that Mildred has been coming back at night to visit her food bowl.  When they keep a watch for her, they discover where Mildred has been hiding and the reason why. 

Seeing Mildred’s adorable new kittens makes the other boys discover a new love of cats and take back all the disparaging things they said about Mildred earlier.

The book is currently available online through Internet Archive.