PLA itself falls in the category of non-conductors, with a resistivity in the order of 10^16 ohm*m (see here), similar to other plastics. Following image gives an idea of the values of resistivity for usual conductors and isolators, insulating materials have resistivity greater than 10^9 ohm*m, conductors have it smaller than 100 ohm*m (copper is about 10^-8 ohm*m).
However, PLA can be mixed with some amounts of a conductor as graphite, making the filament a conductive material (not as good as, by example, copper). This filament can be used to create some kinds of electric circuits.
Other additions (coloring, ...) could also change slightly its properties.
Obviously, if PLA reaches glass transition temperature or melting point holes can appear in the surface, breaking insulation.