I'm trying to add info for the Medical Care Insurance section on the State Taxes but am unsure about what info to include. Is this information provided on the W-2?

What state are you filing in, and what specific question about medical insurance are you trying to answer? Every state is different.

Boxes 5 and 6 on your W-2 are for federal Medicare tax that you pay. They have nothing to do with medical insurance that covers your own medical expenses.