Is there an accepted, or published, protocol for a first contact event?

I rewatched Arrival recently and that prompted this question. There is also an example like the protocol for the Queen's death which involved large swathes of society and had specific intended results: quell potential disturbances, control media response, clarify succession and international context.

A first contact event (at least one that is public) would, presumably and obviously, be a far bigger deal. It would require coordination of the military and civil society organizations/agencies on an international, literally species wide, scale.

Has there been a protocol published? Is there one that exists in the sphere of the UN, or the various space agencies, or one that exists on the level of an individual government? Presumably, we shouldn't just let sci-fi movies be our guide and this is something the public have an interest in (considering the event would likely involve the complete alteration of civil society).