We present a clustering method to extract the depth of interaction (DOI) information from an 8 mm thick crystal version of our continuous miniature crystal element (cMiCE) small animal PET detector. This clustering method, based on the maximum-likelihood (ML) method, can effectively build look-up tables (LUT) for different DOI regions. Combined with our statistics-based positioning (SBP) method, which uses a LUT searching algorithm based on the ML method and two-dimensional mean-variance LUTs of light responses from each photomultiplier channel with respect to different gamma ray interaction positions, the position of interaction and DOI can be estimated simultaneously. Data simulated using DETECT2000 were used to help validate our approach. An experiment using our cMiCE detector was designed to evaluate the performance. Two and four DOI region clustering were applied to the simulated data. Two DOI regions were used for the experimental data. The misclassification rate for simulated data is about 3.5% for two DOI regions and 10.2% for four DOI regions. For the experimental data, the rate is estimated to be approximately 25%. By using multi-DOI LUTs, we also observed improvement of the detector spatial resolution, especially for the corner region of the crystal. These results show that our ML clustering method is a consistent and reliable way to characterize DOI in a continuous crystal detector without requiring any modifications to the crystal or detector front end electronics. The ability to characterize the depth-dependent light response function from measured data is a major step forward in developing practical detectors with DOI positioning capability.