Yes! Even if you find a nanny through word of mouth, you want to have a contract that ensures everything you have agreed to is in writing. At best it will simply serve as a reference for each party to remember what was agreed to, and at best it will protect you in the event you need to fire her for cause or you have irreconcilable differences that require you to part ways gracefully.
There are lots of contract templates available online, but many of them are extremely basic, and you really want a comprehensive agreement, so that when inevitable issues come up (snow days??) you aren't forced to negotiate or make a call on the spot, that your nanny didn't necessarily agree to. Try this one:http://www.thechildcarevillage.com/product/nanny-work-agreement/
Use the code ccarev02 to get the download for free!
Best of luck!