We are developing a high-resolution, high-efficiency positron emission tomography (PET) detector module with depth of interaction (DOI) capability based on a lutetium oxyorthosilicate (LSO) scintillator array coupled at both ends to position-sensitive avalanche photodiodes (PSAPDs). In this paper we present the DOI resolution, energy resolution and timing resolution results for complete detector modules. The detector module consists of a 7 x 7 matrix of LSO scintillator crystals (1 x 1 x 20 mm3 in dimension) coupled to 8 x 8 mm2 PSAPDs at both ends. Flood histograms were acquired and used to generate crystal look-up tables. The DOI resolution was measured for individual crystals within the array by using the ratio of the signal amplitudes from the two PSAPDs on an event-by-event basis. A measure of the total scintillation light produced was obtained by summing the signal amplitudes from the two PSAPDs. This summed signal was used to measure the energy resolution. The DOI resolution was measured to be 3-4 mm FWHM irrespective of the position of the crystal within the array, or the interaction location along the length of the crystal. The total light signal and energy resolution was almost independent of the depth of interaction. The measured energy resolution averaged 14% FWHM. The coincidence timing resolution measured using a pair of identical detector modules was 4.5 ns FWHM. These results are consistent with the design goals and the performance required of a compact, high-resolution and high-efficiency PET detector module for small animal and breast imaging applications.