We present an experimental and theoretical investigation of the influence of the transverse magnetic field (TMF) on the coherent population trapping resonances obtained on the Zeeman sublevels of the D 1 line of 87 Rb in a paraffin-coated vacuum cell. It is shown that a TMF changes the shape and sign of the resonance or destroys it completely. The role of the different rank polarization moments in the integral registered fluorescent signal in the presence of stray magnetic fields is clarified using numerical simulations.