In the US if the police have probable cause and can obtain a warrant then they will be able to obtain the details from financial institutions to track the purchases on a particular credit card.
Can police look into your bank account?
Ordinarily, police departments cannot access personal bank account information, which is protected by key privacy rights in the United States (laws for accessing banking information may work differently in the UK, for instance).
Can police find out who stole your credit card?
Rarely. Not because the police don't want to, but because they simply can't. Just remember that the police generally won't do much if it is a small isolated incident, so be sure to talk to your credit card issuer for help instead.