The experimental set-up for investigation of the rotational and vibrational state distribution of desorbing hydrogen molecules is described. Resonance enhanced multiphoton ionization is applied for this purpose. In a (2+1) process hydrogen molecules are excited into the E, F state and subsequently ionized. Detection of the ions is accomplished by the use of a time-of-flight spectrometer. Performance of the set-up is demonstrated on hydrogen molecules desorbing from nickel using a permeation source. Quantitative determination of the quantum state distribution is attained by comparing the data to the resonance enhanced multiphoton ionization spectra of a Knudsen source. The experiments revealed rotational cooling of the desorbing molecules but no significant change in the vibrational state distribution.