No, you'll only need virus protection for Windows. You don't need to bother with installing an antivirus program on OS X.
I've had Windows installed on my Mac since day one and I have yet to experience any issues. All I did was install AVG antivirus and I was done with it. Nothing to it, really.
You can save yourself a lot of trouble if you simply follow some safety precautions when using Windows on your Mac. Just use the program that you need and not much of anything else. Also, use Firefox instead of Internet Explorer to cut the risk of adware/spyware. And don't download anything in Windows, save it for the OS X side, that way you can prevent getting any viruses.
Best method would be to run Windows side-by-side with OS X. That way you can do your normal stuff like browsing the web and checking your email in OS X, where you have a 0% chance of getting infected with something, and then using that sole Windows program via Parallels or VMWare Fusion. With Windows not doing anything besides running that one program you need, there's really no chance of getting infected with anything.