You can take the time and alert the authorities, but you will likely find out as I did that nothing is done. I filed a complaint through the Internet Crime Complaint Center. I never heard anything.
I went through a similar situation a while back where I was selling a computer component and posted it to Craigslist. A user contacted me, asked me to hold it, said he was on his honeymoon and would send me a check ASAP and then stop by and pick it up. Well, after a few days, I received a UPS envelope and it contained a check, not for the amount of the hardware sold $2,200, but instead for $4,600. The user contacted me via email shortly after receiving it and claimed that his secretary screwed up (and he should fire her for it), but new that I could handle the situation (with care and honesty). He provided instructions saying to immediately deposit it into my bank account, and then simply return the excess fund (minus of course $100 for my effort), as a Money Gram which his "shipper" would pick up when they came for the hardware.
If the above information didn't scream scam, for good measure, I did a little research on the check that I received. It was a business check and was written against a Company name (which had nothing to do with my transaction) and it was signed by a person that I wasn't dealing with. For fun, I looked up the company against which the check was written and talked to their secretary who informed me that the check that I received was fake, their information had been compromised and they had at least 50 fake checks written against their account. As she said, it won't clear..I hope you didn't cash it. I informed her that I did not.
So, in the case of this scam, had I cashed this $4,600 check...my bank would have given me $4,600. I would have then purchased a $2,300 money order, sent it back to this person. A day or two later, when the check moved along it's way, it would have been declared a fake, and my bank would then remove the $4,600 they put into my account. And there is nothing you can do, once you purchase a Money order to get that money back. So, I would have been out $2,300 had I proceeded.
At the end of the day, i got some nasty emails from this person saying they knew my personal information (he had a cell number and my work address...along with my hotmail account) and would come after me. Also got some emails from the shipper claiming they were nearly at my location for the pickup and if I provided them nothing, I would be legally obligated to pay them for their time and effort to get to me.