We present an open-source web service for Czech morphosyntactic analysis. The system combines a deep learning model with rescoring by a high-precision morphological dictionary at inference time. We show that our hybrid method surpasses two competitive baselines: While the deep learning model ensures generalization for out-of-vocabulary words and better disambiguation, an improvement over an existing morphological analyser MorphoDiTa, at the same time, the deep learning model benefits from inference-time guidance of a manually curated morphological dictionary. We achieve 50% error reduction in lemmatization and 58% error reduction in POS tagging over MorphoDiTa, while also offering dependency parsing. The model is trained on one of the currently largest Czech morphosyntactic corpora, the PDT-C 1.0, with the trained models available at https://hdl.handle.net/11234/1-5293. We provide the tool as a web service deployed at https://lindat.mff.cuni.