The 1975 Roman Missal has “The priest then places ashes on those who come forward, saying to each …”.
But in the Book of Blessings, there is an adaptation for the dicoeses of the USA.
“1659. This rite may be celebrated by a priest or deacon who may be assisted by lay ministers in the distribution of ashes. The blessing of the ashes, however, is reserved to a priest or deacon.”
(Book of Blessings, Liturgical Press, ISBN 0-8146-1875-8, page 621)
My understanding is that this was approved by the Vatican on 27 January 1989. It is not part of the original 1984 De Benedictionibus, but an approved adaptation for the USA. On 19 March 1989 the president of the USA’s National Conference of Catholic Bishops wrote that the Book of Blessings could be used from 1 October 1989. From 3 December 1989 its use was mandatory in the USA.
The rubrics of the 2002 Roman Missal describes the priest placing the ashes: “Deinde sacerdos imponit cineres omnibus astantibus, qui ad ipsum accedunt, dicens singulis: …”. (Missale Romanum, page 198). It could be argued that since this has been published more recently it should be followed, even in the USA.
Others could argue that the USA intends to get an approved adaptation to its translation of these rubrics.