This paper presents the first iteration of two connected Ojibwe constraint grammars, one for morphological disambiguation and one for syntactic parsing. Due to the polysynthetic nature of Ojibwe, along with its status as a low-resource language, the disambiguation grammar proves to be an effective and resource-efficient tool for morphological disambiguation, successfully eliminating 32% of redundant readings and fully resolving 41% of ambiguous tokens. The dependency grammar focuses on assigning dependency relations to model argument structure, where the constraint grammar once again proves to be an effective paradigm, with F1 scores of 0.97 for subject and 0.94 for object relations. The rule-based design of both grammars is linguistically informed, allowing for precise modeling of language-specific phenomena such as animacy, obviation, and verb-argument agreement. Applications of the two constraint grammars include building a disambiguated morphologically-tagged corpus of the Ojibwe language and creating a treebank for the Ojibwe language following the widely adopted CoNLL-U format.