The ever-growing amount of sensor data from machines, smart devices, and the environment leads to an abundance of high-resolution, unannotated time series (TS). These recordings encode recognizable properties of latent states and transitions from physical phenomena that can be modelled as abstract processes. The unsupervised localization and identification of these states and their transitions is the task of time series state detection (TSSD). Current TSSD algorithms employ classical unsupervised learning techniques, to infer state membership directly from feature space. This limits their predictive power, compared to supervised learning methods, which can exploit additional label information. We introduce CLaP, a new, highly accurate and efficient algorithm for TSSD. It leverages the predictive power of time series classification for TSSD in an unsupervised setting by applying novel self-supervision techniques to detect whether data segments emerge from the same state. To this end, CLaP cross-validates a classifier with segment-labelled subsequences to quantify confusion between segments. It merges labels from segments with high confusion, representing the same latent state, if this leads to an increase in overall classification quality. We conducted an experimental evaluation using 405 TS from five benchmarks and found CLaP to be significantly more precise in detecting states than six state-of-the-art competitors. It achieves the best accuracy-runtime tradeoff and is scalable to large TS. We provide a Python implementation of CLaP, which can be deployed in TS analysis workflows.