I'm not sure about transferring from the states but I can't imagine that it's any different than from the UK.
You can open a standard Serbian dinar (rsd) account and you can also open a foreign account (or several) in your preferred currency which I'm guessing would be dollars?
A word of warning though, whilst you can withdraw dollars from your account with no charges incurred, if you make a payment from your USD account, even though you might pay in USD (i.e. to an American company) you will incur charges because it leaves your Serbian USD account, get's converted into euros and then gets converted at the other end once again from euros to USD.
I've been stung a couple of times.