akmac - 6:38 pm on Aug 5, 2011 (gmt 0)
Yes, I've collaborated with police a number of times. I think a police response is dependent largely on the value of the attempted or actual theft. Over $500 (I believe) is a felony in the US, anything less and you'll likely get less attention.
At the very least, call the actual card-holder and let them know that their information has been stolen. As much of a pain as it is for merchants, it's often an even larger pain for those whose account numbers (at least) or identities have been stolen.
Theft with a ship to: address in the US is always worth a call to the local PD. 9 times out of ten, it will be a lonely lady helping out her fiancè she's never met (who happens to live in EgyptVietnamIndonesiaNigeriaGhana) by either fencing the goods and sending the money, or re-shipping the actual goods. She needs a wake-up call, and the police do a good job of it. Sometimes, they intercept packages. If you're lucky, it's yours.
I recently got burned for the first time in almost 10 years selling online. Full stolen identity, so the purchase information I had matched exactly the information the bank had. I shipped the $5000 item, and only learned it was a fraudster when the guy whose identity had been stolen called us to let us know it wasn't his order. I called the local PD to let them know, and they had had an earlier complaint from a merchant about the same address, had begun an investigation, and had been intercepting the packages. They had my item. A few weeks later, after faxing a few forms, I had the item back.
If that other merchant hadn't called the police, I would be out thousands on that fraudulent order.
If the ship to: address is in the US, call the police.