and a major medical policy? I carry liability on the policy and have a separate major medical on myself.

In New Jersey you do.In California you do not. It is called personal Injury protection (PIP). PIP has increased ny insurance by about 800 dollars . I paid 600 for my complete coverage for my SUV in cal. When i moved to NJ my insurance more than doubled to 1400

yes, you should still carry medical. most insurance companies make you now days but I have $2000 medical on mine and I still have complete health coverage. You never know if some thing falls through the cracks and you need it. Like Ambulance transport righ toff the bat is like $400 and you health coverage may not cover.
Better safe than sorry.