Depositing very thin organic films on the surface of arrays of asymmetric split-ring resonators (A-SRRs) produces a shift in their resonance spectra that can be utilized for sensitive analyte detection. Here we show that when poly-methyl-methacrylate (PMMA) is used as an organic probe (analyte) on top of the A-SRR array, the phase and amplitude of a characteristic molecular Fano resonance associated with a carbonyl bond changes according to the spectral positions of the trapped mode resonance of the A-SRRs and their plasmonic reflection peaks. Furthermore, we localize blocks of PMMA at different locations on the A-SRR array to determine the effectiveness of detection of very small amounts of non-uniformly distributed analyte.