A dual-layer offset (DLO) detector enables depth-of-interaction (DOI) through light sharing between two layers of scintillation arrays with a single-ended readout (SER) scheme. However, the SER scheme in DLO detectors may lead to a layer misassignment when inter-crystal scattering occurs. The aim of this work is to study inter-crystal scattering and evaluate the effects of layer misidentifications in DLO detectors on the performance of scanners suitable for a brain-dedicated PET insert. The influence of layer misidentification on the coincidence response functions (CRFs) of 3 different DLO detectors with total/front/back layer thicknesses of 15/6/9 mm, 20/8/12 mm, and 25/7.5/17.5 mm and a crystal width of about 3 mm was studied through Monte Carlo simulations. To overcome layer misidentification, we studied a practical DLO detector design in which each layer can be read out independently through a discrete-layer readout (DLR) scheme where light sharing between the layers is avoided. The CRFs of the mentioned DLO detectors assuming SER and DLR were analyzed. To evaluate the effects of layer misidentification on image quality, images of a Derenzo-like phantom were also reconstructed for all DLO and their equivalent single layer PET scanners. Our analysis showed that layer misassignments due to inter-crystal scatter in DLO detectors mainly has effect on the full-width at tenth maximum of the CRFs. According to the reconstructed images of the phantom, no significant improvements in the quality of the images were seen when SER was replaced with DLR. The results suggest that layer misidentification in DLO detectors does not play an important role in the quality of the PET images.