Somewhat resembling 'immune'(ty). Coincidence?
I bothered to search here: https://translate.google.com/#el/en/%CE%BC%CF%85%CE%BD%CE%B1 But the answer seemed misguiding.
It is a coincidence. Actually it comes from immunis in latin =in (=not)+munis (=performing services) which is related with munincipal. Immunis had a meaning of "exempt from public service, untaxed". Exempt from disease came as a later meaning.