Q: A stray dog ran into my property and animal control tranquilzed her while on my Property and trespassed to catch her

A: Probably not. The U.S. and state constitutions prohibit entry into homes without warrants unless a person consents to the entry or exigent circumstances exist. Pursuing a stray dog will often result in the dog entering or crossing private property, as dogs tend to not respect property lines. California has attempted to address this claim by statute. If a dog has strayed and then returned to its homed, but no one is home at the residence, the officer may enter the property to obtain the dog for impound. In that case, the officer must leave notice of the impound. Such notice shall state the following: that the dog has been impounded, where the dog is being held, the name, address, and telephone number of the agency or person to be contacted regarding release of the dog, and an indication of the ultimate disposition of the dog if no action to regain it is taken within a specified period of time by its owner or by the person who has a right to control the dog. https://codes.findlaw.com/ca/government-code/gov-sect-53074.html

Unfortunately, this statute does not address whether Animal Control can enter the property of someone who does not own the dog. In Conway v. Pasadena Humane Society , 52 Cal.Rptr.2d 777 (Cal.App. 2 Dist.,1996), the court considered whether animal control officers can lawfully enter a home, without a warrant or consent by the owners, to seize and impound the homeowner's dog for violation of a leash law. The court held that the Fourth Amendment precludes such conduct.

In your case, a finding of exigent circumstances may depend on the nature of the dog in question. Was it vicious? Had it bitten someone or another dog? Was the public's safety at issue?