Chomsky Hierarchy and P vs NP

Question

I have read multiple questions here that involve this kind of subject but I haven't found any definite answer. In what class do regular languages belong? (P or NP or some regular are P and other NP), context-free languages? (same question) ,context-sensitive? and general languages? . I personally believe all regular languages belong in P class and the rest (more complex) languages of chomsky hierarchy are in the NP class. Can someone answer and provide some kind of proof for the answer? Thanks in advance.