The interaction of the adiabatically tapered photonic crystal fiber fundamental mode with a thin-film absorbing coating, deposited on a surface of a taper waist, on transmission of a tapered fiber is studied. Examples of using this interaction in refractive index sensors and for detection of an adsorption layer with ammonia molecules upon contact of the absorbing coating with a liquid medium are presented. It is obtained that a pronounced sensory effect occurs in the case of a resonant coupling between the fundamental fiber mode and cladding modes localized between photonic crystal fiber air channels and the absorbing coating.