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I haven't really seen anything similar to Midsomer Murders. Even when you search online for Midsomer Murders alternatives they really aren't similar.
If you install both the free Filmrise BritishTV and Fawesome BritishTV Channels (from Streaming Channels...Search Channel..."BritishTV" both these Channels will show), gives you a lot of different detective murder mystery series.
Most of my family members watch Midsomer Murders and always argue whether any other show is better or even similar to that one, so good luck in your Searching.
Roku Community Streaming Expert Just another Roku user... I am not a Roku employee.