We study the connection of star formation to atomic (HI) and molecular hydrogen (H2) in isolated, low metallicity dwarf galaxies with high-resolution SPH simulations. The model includes self-gravity, non-equilibrium cooling, shielding from an interstellar radiation field, the chemistry of H2 formation, H2-independent star formation, supernova feedback and metal enrichment. We find that the H2 mass fraction is sensitive to the adopted dust-to-gas ratio and the strength of the interstellar radiation field, while the star formation rate is not. Star formation is regulated by stellar feedback, keeping the gas out of thermal equilibrium for densities n < 1 cm-3. Because of the long chemical timescales, the H2 mass remains out of chemical equilibrium throughout the simulation. Star formation is well-correlated with cold gas, but this dense and cold gas - the reservoir for star formation - is dominated by HI, not H2. In addition, a significant fraction of H2 resides in a diffuse, warm phase, which is not star-forming. The cold gas fraction is regulated by feedback at small radii and by the assumed radiation field at large radii. The decreasing cold gas fractions result in a rapid increase in depletion time (up to 100 Gyr) for total gas surface densities, in agreement with observations of dwarf galaxies in the Kennicutt-Schmidt plane.