Magnetic field measurements above type-II superconductor films in a remanent magnetization state have been used to determine two dimensional surface current distributions. Using the Biot-Savart law for the surface current density, integral equations (of 2-D convolution type) for two components of current have been obtained. These equations have been solved by employing Tikhonov's method of generalized discrepancy, and the surface current pattern in superconductors as well as the magnetic field distribution on the film surface have been obtained. Current peculiarities related to various kinds of inhomogeneities, specific character of the film form, and a laser pulse effect have been observed. In particular, it was discovered that a laser pulse can signficantly redistribute the film currents without changing the total number of current vortices in the film.