Not by the state. What the state does have is a home inspection licensing law that says a home inspection shall not include an inspection for radon or pests, and standards of practice that say home inspectors are not required to determine the presence or absence of wood destroying organisms. Your seller's Property Condition Disclosure Statement asks whether there is any termite, insect, rodent or pest infestation or damage, and the seller answers based on their actual knowledge at the time of signing. Neither one is an inspection.
The requirement, when there is one, comes from the lender. The VA's local requirements for New York list Nassau, Suffolk, Queens, Bronx, and the rest of the metro counties as places where wood destroying insect information is required. HUD's guidance for FHA loans is that an inspection is required if there is evidence of active infestation, if mandated locally, if customary to the area, or at the lender's discretion. Ask your loan officer early; a report ordered the week of closing is the one that delays it.