While there potentially is a way to set this do what you are asking, the challenge will come with if you or someone else changes the dropdown status. It would be easier to have the checkbox for complete auto check when the dropdown says complete. If you populate a dropdown field with a formula, then manually choose a dropdown option, it will overwrite the formula and would stop working. I would stick with marking items as complete via the dropdown or come up with a method for checkboxing the other status' so that no one is manually setting any of the dropdown statuses. Does that make sense? 

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