Unless the dogs are somewhat special (meaning worth a lot of money) the police will only investigate it as a misdemeanor. However, if you are well enough off you can find a PI for pets (kind of like Ace Ventura (I know, I know) to do some private investigating. The steps to do it yourself are a bit too much to explain in a Google Q&A, but ur best bet is a PI or get someone to 1) draw out any faces you remember, and 2) stake out the area or similar areas nearby for the people using seemingly the sane tactic, etc and for the faces drawn from your memory. Also, find any nearby cameras and ask the owners for the clip of the time of the incident and a few minutes before to maybe see them walking by. Good luck!
Definitely call the police asap!
If you recognize the thief call the police and report it. What kind of a dog was in it and where were you walking?
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