Best practices for high conflict conversations like counseling or customer support almost always include recommendations to paraphrase the previous speaker. Although paraphrase classification has received widespread attention in NLP, paraphrases are usually considered independent from context, and common models and datasets are not applicable to dialog settings. In this work, we investigate paraphrases in dialog (e.g., Speaker 1: "That book is mine." becomes Speaker 2: "That book is yours."). We provide an operationalization of context-dependent paraphrases, and develop a training for crowd-workers to classify paraphrases in dialog. We introduce a dataset with utterance pairs from NPR and CNN news interviews annotated for context-dependent paraphrases. To enable analyses on label variation, the dataset contains 5,581 annotations on 600 utterance pairs. We present promising results with in-context learning and with token classification models for automatic paraphrase detection in dialog.