Azure Cosmos DB is a globally distributed multi-model database with support for multiple APIs. This is a link to an article which describes how to use REST to query resources using the Azure Cosmos DB API – https://docs.microsoft.com/en-us/rest/api/documentdb/querying-documentdb-resources-using-the-rest-api

All Cosmos DB resources (with the exception of account resources) can be queried using Azure Cosmos DB SQL language. See Query with Azure Cosmos DB SQL for additional details on syntax – http://azure.microsoft.com/documentation/articles/documentdb-sql-query

For a full sample using .NET visit https://github.com/Azure/azure-documentdb-dotnet/tree/master/samples/rest-from-.net