As long as the giver believes the recipient to be a legal owner of the gun, yes. However, I do think you now need to involve a FFL dealer to do an over-the-counter transfer. Not all dealers will.
EDIT: There may be a case where that's not necessary. Per the official online hosting of Colorado Revised Statutes (direct link to the Statute here),
(6) The provisions of this section do not apply to:....
(b) A transfer that is a bona fide gift or loan between immediate family members, which are limited to spouses, parents, children, siblings, grandparents, grandchildren, nieces, nephews, first cousins, aunts, and uncles;