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Blockchain has emerged as a decentralized and distributed framework that enables tamper-resilience and, thus, practical immutability for stored data. This immutability property is important in scenarios where auditability is desired, such as in maintaining access logs for sensitive healthcare and biomedical data.However, the underlying data structure of blockchain, by default, does not provide capabilities to efficiently query the stored data. In this investigation, we show that it is possible to efficiently run complex audit queries over the access log data stored on blockchains by using additional key-value stores. This paper specifically reports on the approach we designed for the blockchain track of iDASH Privacy & Security Workshop 2018 competition.Particularly, we implemented our solution and compared its loading and query-response performance with SQLite, a commonly used relational database, using the data provided by the iDASH 2018 organizers. Depending on the query type and the data size, the run time difference between blockchain based query-response and SQLite based query-response ranged from 0.2 seconds to 6 seconds. A deeper inspection revealed that range queries were the bottleneck of our solution which, nevertheless, scales up linearly. Concretely, this investigation demonstrates that blockchain-based systems can provide reasonable query-response times to complex queries even if they only use simple key-value stores to manage their data. Consequently, we show that blockchains may be useful for maintaining data with auditability and immutability requirements across multiple sites.