Neighbors oak tree is growing over my roof causing problems. Is it his responsibility to trim the tree ?

Actually, even though it is your neighbor's tree, you have the right to cut any branches that overhang your yard. Your neighbor would be trespassing if he entered your property to trim the tree, so if you want him to help pay for the tree trimming, I suggest you get a couple of estimates and ask him to share the expense with you. If you are concerned about the damage to the roof, it would be advisable to take care of this, even if the neighbor refuses to help.

Be careful about any self help measures you take. You would be responsible for damage to his property. There may also be nuisance ordinances that would help you. But neighborly cooperation is the first step, as first suggested.