The effect of tip asymmetry on atomic-resolution scanning tunneling microscopy and atomic force microscopy measurements of graphitic surfaces has been investigated via numerical simulations. Employing a three-dimensional, crystalline, metallic tip apex and a two-layer thick graphene sample as a model system, basic calculations of the tip-sample interaction have revealed a significant effect of tip asymmetry on obtained results, including artificial modulation of site-specific chemical interaction forces and spatial distortion of observed features. Related artifacts are shown to be enhanced for tips with low lateral stiffness values. Our results emphasize that potentially erroneous interpretations of atomic-scale surface properties via imaging and spectroscopy measurements can be caused or enhanced by tip asymmetry.