If your credit card is stolen then yes police will investigate the theft of the credit card especially if your credit card has been used.
However the police cannot do much about the credit card theft if they don't know who actually used your credit card.
When you get your credit card stolen or lose the credit card you need to call the credit card company immediately and report the credit card as lost or stolen and they will shut the credit card down so that it cannot be used.
The credit card company will then issue you a new one while deactivating that one.
And then if someone uses the credit card after you've called them and reported that credit card lost or stolen then you won't be liable for those charges on the credit card.
It can be hard to find out who exactly used your credit card or stolen it if you don't know who did it.
But you should still go to the police department and make a report on the theft of your credit card so that they have it on record and sometimes they find the person while other times they do not.