I was just wondering if it is legal to shoot squirrel inside of the city limits? I live in Austin Texas and can't find a site for my local game laws. So if anyone can help let me know.

State & local laws vary quite a bit.
Most hunting laws were written a long time ago and some have limits on how far you can hunt from a populated area and airguns usually were not considered when the laws were written.

There is a web site that lists all 50 States DNR web sites.
But if you are after city laws, which you should check because some places do not allow shooting airguns in city limits.

It would be best just to call your local Police and ask them or see if your local Libary offers a search to find City laws. A lot of them do it for free.

Art

Over here, in The Netherlands, Europe, you can't shoot anything
unless it's in your own backyard.

I've shot a pidgeon out of a tree with my old Crosman 622 and the next
day the police were on my doorstep.

I didn't get a fee for this, because I didn't know the rules nor the laws
and they kept it with a warning.

So unless you have a big backyard with some trees and squirells in there, you can't shoot em :-D.

u can pretty much shoot squirrels and rabbits anytime with airguns you canot hun them anytime with guns i know squirrel season is in 5 months its twice befor deer season and after dear season.