Is it permissible for a Muslim doctor to sign a cremation certificate for a deceased person, if the law in their country allows it and stipulates their approval?

It is not permissible to sign for the cremation of a deceased Muslim, as this falls under cooperation in sin and aggression. As for a disbeliever, the more cautious approach is not to sign for their cremation due to its lack of legitimacy, but if one is compelled to do so, then the matter is easy in the case of a disbeliever.