I'm writing to ask about ability of using this image for a castration program logo for my county.
You can use it as an icon, mascot, or supporting graphic without asking for permission. This note is your permission to use it for the purposes you've stated "for a castration program logo" for your county. The only thing you need to know is that the logo will not be able to be exclusively copyrighted or trademarked by you and will not be legally protected like original works because it is freely available to others (even competitors) to download and use in their publications.
Stockazoo offers royalty free vector files for commercial or personal use