I sold an iPhone 4 on Craigslist yesterday. I had the item listed for $375 and accepted his offer of $340. The guy looked at the phone, went through all the features and software information. The wi-fi didn't work which was stated several times while he was looking through it. After looking through the phone he said he would take it and handed me the money. About 2 hours later I keep getting phone calls him saying he wants to return the phone back to me and get his money back and he is showing up at my home. I told him I would not do a refund and now he is trying to sue me... Am I obligated to do a refund? Or does he now own the phone? I thought all sales were final on Craigslist unless stated otherwise and they are "as is". What do you think?

He paid for it; he took it,now he owns it. Tell him that.

Buyer be ware, unless you gave a written warranty items are sold "as is" what you see is what you get. 99.9% of the people who say tey will sue do not, the remainung .1% are just nuts cases.

At the time of the sale was the phone in the same condition as was stated on Craigslist ? Did it appear in the ad that the wifi feature wasn't working?

Craigslist doesn't have consumer laws, your state does. Some do have laws about returns within 3 days, for example, and various lemon laws for cars, etc.
As for suing, anyone can sue anyone. Whether he wins or not, who knows, but I suspect he wouldn't.
It sounds like he didn't know what it meant to have a nonworking wifi.