Are cops allowed to lie when they're interrogating suspects?

I was called to the police department the other day without being given a reason why. As soon as I showed up I was treated like a criminal. Apparently one of my neighbor's got his beer stolen and he told the cops it was me (this neighbor doesn't like me for some reason). So the investigator (major league jerk) starts informing ME what I did that night, and it convoluted into the most laughably implausible story I had heard in my life. "Your dad's asleep, YOU sneak out, and you have your friend's phone..." Evidently I had somehow gotten a hold of my friend Erik's phone (despite that he's three hours out of town) and used it to text other people about stealing his beer, signed my own name, then personally stole his beer. Of course I didn't nod and smile the whole time, I told him this was all false and I got called a y smart. He talked down to me, then asked me random things like whether I had a girlfriend, then took my prints and said he'd compare them later that day. But I haven't gotten any word back. I really doubt they compared those prints, because I don't think anyone believes that story. I don't know what action I should take at this point because I don't know whether the investigator's behavior was technically legal or not. Advice?