This answer was collected from TheMufti.com, which is a fatwa portal managed by Mufti Ismaeel Bassa from South Africa.

How should a Muslim greet a non-Muslim?

Answered by TheMufti.com

Q. How do I respond to my non-Muslim staff who great me with Assalaamu Alaikum? A. As a general rule, a Muslim should not initiate the official greeting of a Muslims Salaam with non-Muslims. One of the main reasons being that the official greeting of Muslims –Salaam, is a Dua (supplication) that encompasses a Dua… read more »