Deep learning (DL) models, especially those large-scale and high-performance ones, can be very costly to train, demanding a great amount of data and computational resources. Unauthorized reproduction of DL models can lead to copyright infringement and cause huge economic losses to model owners. Existing copyright protection techniques are mostly based on watermarking, which embeds an owner-specified watermark into the model. While being able to provide exact ownership verification, these techniques are 1) invasive, as they need to tamper with the training process, which may affect the utility or introduce new security risks; 2) prone to adaptive attacks that attempt to remove the watermark; and 3) not robust to the emerging model extraction attacks. Latest fingerprinting work, though being non-invasive, also falls short when facing the diverse and ever-growing attack scenarios. In this paper, we propose a novel testing framework for DL copyright protection: DEEPJUDGE. DEEPJUDGE quantitatively tests the similarities between two DL models: a victim model and a suspect model. It leverages a diverse set of testing metrics and test case generation methods to produce a chain of supporting evidence to help determine whether a suspect model is a copy of the victim model. Advantages of DEEPJUDGE include: 1) non-invasive, as it works directly on the model and does not tamper with the training process; 2) efficient, as it only needs a small set of test cases and a quick scan of models; 3) flexible, as it can easily incorporate new metrics or generation methods to obtain more confident judgement; and 4) fairly robust to model extraction and adaptive attacks. We verify the effectiveness of DEEPJUDGE under typical copyright infringement scenarios, including model finetuning, pruning and extraction, via extensive experiments on both image and speech datasets with a variety of model architectures.