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Named entity recognition models (NER), are widely used for identifying named entities (e.g., individuals, locations, and other information) in text documents. Machine learning based NER models are increasingly being applied in privacy-sensitive applications that need automatic and scalable identification of sensitive information to redact text for data sharing. In this paper, we study the setting when NER models are available as a black-box service for identifying sensitive information in user documents and show that these models are vulnerable to membership inference on their training datasets. With updated pre-trained NER models from spaCy, we demonstrate two distinct membership attacks on these models. Our first attack capitalizes on unintended memorization in the NER's underlying neural network, a phenomenon NNs are known to be vulnerable to. Our second attack leverages a timing side-channel to target NER models that maintain vocabularies constructed from the training data. We show that different functional paths of words within the training dataset in contrast to words not previously seen have measurable differences in execution time. Revealing membership status of training samples has clear privacy implications, e.g., in text redaction, sensitive words or phrases to be found and removed, are at risk of being detected in the training dataset. Our experimental evaluation includes the redaction of both password and health data, presenting both security risks and privacy/regulatory issues. This is exacerbated by results that show memorization with only a single phrase. We achieved 70% AUC in our first attack on a text redaction use-case. We also show overwhelming success in the timing attack with 99.23% AUC. Finally we discuss potential mitigation approaches to realize the safe use of NER models in light of the privacy and security implications of membership inference attacks.