So, I figured I'd give you some perspective on the financial side of things, since you're getting tons of advice on how to deal with your douchenozzle sister. I won't go into too much detail, since all banks work disputes differently, and I can be fired for giving industry info. However I can give you an overview on what to expect from filing a dispute.

First, a police report isn't required for fraud claims. You don't have to do it to get your money back. You actually didn't even need to call the merchant. If it's a Visa card, their chargeback rights say you don't have to do so. It's a good idea imo, and can help your claim, but it cannot be denied for not having a report.

Second, if you have ever let your sister use your card in the past, you have made her an authorized user for the LIFETIME of that card. Any charges done by her are then authorized, even if she took it straight out of your purse years later. Your bank can and will deny a claim for this.

Third, unless it's an obscene amount of money the bank generally won't try to prosecute. If the claim is a small amount, it's just not worth it. Do you know how much fraud happens daily? It's literally a constant. I don't work in legal, but I can guess that they just don't have time or resources to persecute cases unless it's a TON of money with a clear-cut perp. However, if someone DID commit fraud, the bank has a right to investigate.

If you've never given your sister authorization to use your cards and she took it from you, that is fraud, and you can dispute those changes. PIN transactions are insured by the bank, and signature transactions are insured through Visa (in most circumstances). If they're not, the bank legally has to cover the loss (as long as it's reported within a timely manner. However, you have the shittiest bank ever if they don't cover everything. It's basically industry standard and basic customer service at this point).

Either way, you can file a claim through your bank if it's fraud and the police don't have to be involved. Personally, I'd call the cops on her ass, but that's your choice.

Good luck!