This study explores the effects of different assumptions and systematics on the determination of the local, spatially resolved star formation law. Using four star formation rate (SFR) tracers (Halpha with azimuthally averaged extinction correction, m
id-infrared 24 micron, combined Halpha and mid-infrared 24 micron, and combined far-ultraviolet and mid-infrared 24 micron), several fitting procedures, and different sampling strategies we probe the relation between SFR and molecular gas at various spatial resolutions and surface densities within the central 6.5 kpc in the disk of NGC4254. We find that in the high surface brightness regions of NGC4254 the form of the molecular gas star formation law is robustly determined and approximately linear and independent of the assumed fraction of diffuse emission and the SFR tracer employed. When the low surface brightness regions are included, the slope of the star formation law depends primarily on the assumed fraction of diffuse emission. In such case, results range from linear when the fraction of diffuse emission in the SFR tracer is ~30% or less (or when diffuse emission is removed in both the star formation and the molecular gas tracer), to super-linear when the diffuse fraction is ~50% and above. We find that the tightness of the correlation between gas and star formation varies with the choice of star formation tracer. The 24 micron SFR tracer by itself shows the tightest correlation with the molecular gas surface density, whereas the Halpha corrected for extinction using an azimuthally-averaged correction shows the highest dispersion. We find that for R<0.5R_25 the local star formation efficiency is constant and similar to that observed in other large spirals, with a molecular gas depletion time ~2 Gyr.
