  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 (H\alpha with azimuthally averaged
extinction correction, mid-infrared 24 micron, combined H\alpha 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
H\alpha 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.
