Bright Be star β CMi has been identified as a non-radial pulsator on the basis of space photometry with the MOST satellite and also as a single-line spectroscopic binary with a period of 170. d 4. The purpose of this study is to re-examine both these findings, using numerous electronic spectra from the Dominion Astrophysical Observatory, Ondřejov Observatory, Universitätssterwarte Bochum, archival electronic spectra from several observatories, and also the original MOST satellite photometry. We measured the radial velocity of the outer wings of the double Hα emission in all spectra at our disposal and were not able to confirm significant radial-velocity changes. We also discuss the problems related to the detection of very small radial-velocity changes and conclude that while it is still possible that the star is a spectroscopic binary, there is currently no convincing proof of it from the radial-velocity measurements. Wavelet analysis of the MOST photometry shows that there is only one persistent (and perhaps slightly variable) periodicity of 0. d 617 of the light variations, with a doublewave light curve, all other short periods having only transient character. Our suggestion that this dominant period is the star's rotational period agrees with the estimated stellar radius, projected rotational velocity and with the orbital inclination derived by two teams of investigators. New spectral observations obtained in the whole-night series would be needed to find out whether some possibly real, very small radial-velocity changes cannot in fact be due to rapid line-profile changes.