And Do I Have To Be The Owner Of The Cat? The Cat Got In My House And Killed My Parakeet.

Is It Free To Get A Cat Euthanized? - No
And Do I Have To Be The Owner Of The Cat? - Yes
The Cat Got In My House And Killed My Parakeet. - Sounds more like a legal matter to take up with the owners.

I'm very sorry about your parakeet, but I hope you realize you can't have someone's cat killed because it followed its instinct and killed a bird... I agree with Curlyben that it's a legal matter you should take up with the owners.