We present an analysis of the relation between star formation rate (SFR) surface density ({Sigma}_SFR_) and mass surface density of molecular gas ({Sigma}_H2_), commonly referred to as the Kennicutt-Schmidt (K-S) relation, at its intrinsic spatial scale, i.e. the size of giant molecular clouds (~10-150pc), in the central, high-density regions of four nearby low-luminosity active galactic nuclei (AGN). These are AGN extracted from NUclei of GAlaxies (NUGA) survey. This study is aimed at investigating the correlations and slopes of the K-S relation, as a function of spatial resolution and of different ^12^CO emission lines used to trace {Sigma}_H2_, and testing its validity in the high-density central regions of spiral galaxies. We used interferometric IRAM ^12^CO(1-0) and ^12^CO(2-1), and SMA ^12^CO(3-2) emission line maps to derive {Sigma}_H2_ and HS T-H{alpha} to estimate {Sigma}_SFR_.