If a tenant fails to send back the inquiry form, does the landlord have to take any further steps to determine whether a child of requisite age resides in the apartment?

Yes. The landlord then has a window of time designated by the law to make an inspection to determine whether a child of requisite age resides in the dwelling. If he fails to gain access to perform the inspection, he then must notify a city agency known as the Department of Health and Mental Hygiene of the situation.