What is the ruling on offering condolences to a non-believer upon his death, whether his family are Muslims or non-believers?

If the deceased was a Muslim, there is no harm in offering condolences to their Muslim family. However, if the deceased was a disbeliever, the matter of benefit should be considered. If offering condolences brings affection and unites hearts, then there is no harm. Otherwise, there is no benefit in it.