In Utah, it is illegal to detonate any nuclear weapons but it's OK to own them.

Apparently in Utah you can have nuclear weapons, just not detonate them. An actual group was formed in 2007 called the "Utah Campaign to Abolish Nuclear Weapons".

Their two primary goals are:

1. To have the U.S. lead the world in disarming and ending the production of nuclear weapons.

2. Continued public awareness of nuclear weapons.

(Source)