Where to turn if investigating police officer is not doing anything?

I'd begin speaking with your bank. Letting them know your account has these charges you had not made. Someone there should be able to investigate the charged. They would then involve the police if they saw the need to.

You should speak to your bank. If this is a stranger to you that fruadulently used your account, it is a whole different matter than if it is a relative . Now not legally, of course, but it would explain why teh officer is putting it on the back burner, or they could be overwhelmed. Have you spoken directly to the officer? and his repsonse was?
if it is a relative, LEOs often go to a lot of work bulding a case , then the relative will not prosecute after all,
The finacial strain will nto be resolved by the police, unless there is a conviction and your state allows criminal restitution; a long way off.

you can bring a small claims court action against the person, but that will take time also.
if thoise charges were fradulent , the bank should charge back the accts of those that presented the fraudulent paper.

If you are still unsatisfied, take to the officers commander.