Do I need uninsured motor vehicle bodily injury insurance if I am in a no fault state?

Yes, you need this coverage, especially if you don't have your own health insurance.

The fact that you're in a no-fault state doesn't change this.  While you might get your medical expenses covered on a no-fault basis, depending on your policy, that won't get you any compensation for your lost wages or your pain and suffering.  The uninsured motorist coverage is basically a just-in-case mini-policy for any driver who causes your accident but doesn't have his own insurance to cover the damages.  You're placing a small bet at long odds, that an uninsured driver will hit you, and it's usually a very good value for what it costs.