We have investigated the dielectric behavior of polycrystalline (Ba,Sr)TiO3 thin films deposited by liquid-source metalorganic chemical vapor deposition. The time-domain polarization current, the frequency dependence of the permittivity, and the dielectric loss for these CVD films are all described by a single set of parameters via the phenomenology of Curie - von Schweidler behavior. No change in the general form of the permittivity is found out to 1.5 GHz, suggesting that this description of the response is valid into the frequency range of interest for many applications. Low-frequency dispersion is found to be controllable, leading to films with very low dissipation factors and almost frequency-independent dielectric response. Finally, a non-zero intercept of the inverse of capacitance versus film thickness suggests the existence of a series interfacial capacitance, arising from either microstructural inhomogeneity or energy barriers to carrier transport at the film-electrode interfaces.