Nate the Great and the Halloween Hunt by Marjorie Weinman Sharmat, 1989.

Nate the Great gets a Halloween case when Rosamond asks him to help her find one of her cats.  Rosamond and Annie show up at Nate’s house, trick-or-treating.  They’re both dressed as Little Red Riding Hood, and Annie’s dog, Fang, is the wolf/grandmother.

Rosamond has several cats, all named “Hex”: Big Hex, Plain Hex, Super Hex, etc.  But, she’s worried because she can’t find Little Hex.  Every Halloween, her other cats like to go to an old house in the neighborhood that is supposedly haunted in order to help haunt it, but Little Hex is afraid on Halloween and apparently hid somewhere.  Nate thinks that Little Hex will probably come out as soon as Halloween is over, but Rosamond is so worried that he agrees to look for Little Hex anyway.

Nate interviews kids in the neighborhood to see if they’ve seen Little Hex, but they haven’t.  Then, he and his dog, Sludge, go to the haunted house to look around.  He sees Rosamond’s other cats, but not Little Hex.  There’s a scary moment when he realizes that he’s locked in the house, but Sludge helps him to escape.

Little Hex isn’t as far away or lost as Rosamond thinks, and Nate realizes that both Sludge and Rosamond herself have given him the clues he needs to solve the mystery.  Sludge demonstrates what an animal might do when it’s frightened, and Nate suddenly realizes why Rosamund’s treat basket was so much heavier than Annie’s even though they had been to the same houses.

The book is available to borrow and read for free online through Internet Archive.