Cloud-based machine learning inference is an emerging paradigm where users query by sending their data through a service provider who runs an ML model on that data and returns back the answer. Due to increased concerns over data privacy, recent works have proposed Collaborative Inference (CI) to learn a privacy-preserving encoding of sensitive user data before it is shared with an untrusted service provider. Existing works so far evaluate the privacy of these encodings through empirical reconstruction attacks. In this work, we develop a new framework that provides formal privacy guarantees for an arbitrarily trained neural network by linking its local Lipschitz constant with its local sensitivity. To guarantee privacy using local sensitivity, we extend the Propose-Test-Release (PTR) framework to make it tractable for neural network queries. We verify the efficacy of our framework experimentally on real-world datasets and elucidate the role of Adversarial Representation Learning (ARL) in improving the privacy-utility trade-off.