As long as a piece can stand on its own--can be considered a complete short story...that's fine. I've written book chapters that are in themselves complete, stand alone stories. Those are fine. No to-be-continued, etc.

I could tell (from looking at your profile) that you had written about this cat detective before, but this piece read as a complete story. That's the only requirement. I love your writing (what I've read so far).