How should I handle liability insurance given that I pay local handymen to fix roof leaks and they don't have insurance?

I'm assuming you have homeowners insurance. You should contact your agent or the policy services dept. of your insuring company and discuss this with them, there may not be coverage under your liability portion of your homeowners policy to cover him, and you may want to add an endorsement. Your state insurance department is your best resource for insurance-related questions and concerns. Find information on insurance companies and agents, rate quotes and comparisons, insurance buying tips, claims filing information and much more!

State Insurance Department websites: http://www.naic.org/state_web_map.htm