Did the city have the right to do this?

Long story short—(because I’m on my phone because fluther won’t let me post a question from anywhere but my phone)—the animal officer set a live trap on my property, next to the garage on my drive way, without our permisson
He trappeared my cat and hauled her off to the pound.
It was a 4 day ordeal finding out what had happened and who did it, before I got my cat back.
When the pound said I’d have to pay a fine to the city before I could retrieve her I got hot. And not the sexy kind.
Anyway, the city did waive the fines and I only had to pay $16 for boarding fees to the pound.

Are they allowed to do that?

I’ll add more in the comments when I get back to my laptop or desk top.