No. I just voted about half an hour ago, so the process is still fresh in my mind: When you enter the polling place, you place yourself either at the Democratic or the Republican station. The poll workers at that station look you up on their list (which is either a list of Democratic or Republican voters, respectively) to make sure that you are registered and affiliated as you have said that you are. Once satisfied, they hand you a ballot that lists only the candidates of the party in which you are registered. So if you're not registered as a member of a given party, you can't vote in that party's primary. In the general election in November, of course, it's a whole other ball game, and you can vote for anyone you want, without regard to your party affiliation or non-affiliation.