My old refrigerator just died, so I bought a new one. When the installation people came to remove the old and install the new, they noted that the existing copper water line does not have a shut off vavle on the floor side of the line (in the kitchen), and that their contracts did not allow them to go into the crawl space to do so.

I went into the crawl space and found the water line junction, but the valve did not appear to close... so now I am unsure of what to do. Is it best to have a handyman or a plumber come to take a look and likely add a new shut-off valve in the kitchen?

How much should I expect to pay?

Depends on where you are located and the going local rate. If you use a piercing saddle, it will be cheaper but some codes do not allow it. Also depends on how far from the water supply to the refrigerator and if they have to drill into the crawl space and then come back up. Guestimate? $150-200 for a plumber, $100-150 for a handyman.

Why not buy a kit at Home Depot, Lowe's, or any good hardware store and put it in yourself. You can get one that uses a plastic line (Do not over-tighten fittings on plastic lines.) and you can put it in very easily in a few minutes. It's about as complicated as hooking up a water hose. The kits are about $20.00.