A recent merger of two supermassive black holes (BH) or the presence of a second active BH in the galactic nucleus are two of the main scenarios proposed to explain the X-shaped morphology observed in X-shaped radio galaxies. We test these scenarios by studying the BH mass, radio and optical luminosity, starburst history and dynamic age of radio lobes in a sample of X-shaped radio galaxies and in a control sample of radio-loud active nuclei with similar redshifts and optical and radio luminosities. We find that the X-shaped sources have statistically higher BH mass and older starburst activity than the objects from the control sample. Implications of these findings are discussed for the BH merger scenario and for the potential presence of active secondary BHs in post-merger galaxies