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Monolithic scintillator detectors, consisting of several cm3 of scintillating material coupled to one or more Hamamatsu S8550 avalanche photodiode (APD) arrays, are proposed as detectors for high resolution positron emission tomography (PET). In this work, the factors contributing to the variance on the signals are investigated, and their effects on the energy, time and spatial resolutions are analyzed. Good agreement was found between a model of the energy resolution and experiments with a 20 x 10 x 10 mm3 LYSO:Ce crystal coupled to a single channel large-area APD (LAAPD). With the same crystal coupled to an APD array, differences between model and experiment were observed at high APD gain. The measured energy resolution of ~11% FWHM was dominated by scintillation photon statistics, with less important roles for the APD excess noise factor and electronic noise. On the other hand, electronic noise was an important factor both for the time and the spatial resolutions. The time resolution was found to depend strongly on the APD bias voltage, and was best at the highest bias. A time resolution of 1.6 ns full width at half maximum (FWHM) was measured against a BaF2 -PMT detector. The best spatial resolution measured was 1.64 mm FWHM, without correction for the ~0.9 mm FWHM measurement beam. It is estimated that an intrinsic spatial resolution of 1.26 mm FWHM can be achieved at the center of the detector with an infinitely narrow test beam.