Went on an interview, and they called 3/4 references. It's been 2wks no word. What should I do?

I applied for a city and county position, and went on a few interviews. The initial was a phone interview and written test, then an in person interview, which was a 3 person interview panel. Finally, I was asked back for an in person interview with the department supervisor. I confirmed that 3 of my 4 references were contacted and they said it sounded promising for me. During my interview with the department supervisor, he mentioned I would hear back either way, but I'm eager to start. It's been two weeks since my references were contacted. Should I email the department supervisor?