We use atomic force microscopy (AFM) to perform a systematic quantitative characterization of the elastic modulus and dielectric constant of poly(L-lactic acid) electrospun nanofibers (PLLA), as well as composites of PLLA fibers with 1.0 wt% embedded multiwall carbon nanotubes (MWCNTs-PLLA). The elastic moduli are measured in the fiber skin region via AFM nanoindentation, and the dielectric constants are determined by measuring the phase shifts obtained via electrostatic force microscopy (EFM). We find that the average value for the elastic modulus for PLLA fibers is (9.8 ± 0.9) GPa, which is a factor of 2 larger than the measured average elastic modulus for MWCNT-PLLA composites (4.1 ± 0.7) GPa. We also use EFM to measure dielectric constants for both types of fibers. These measurements show that the dielectric constants of the MWCNT-PLLA fibers are significantly larger than the corresponding values obtained for PLLA fiber. This result is consistent with the higher polarizability of the MWCNT-PLLA composites. The measurement methods presented are general, and can be applied to determine the mechanical and electrical properties of other polymers and polymer nanocomposites.