In Manu Smriti, there is no reference about a Girl being initiated through Upanayanam.
In Manu Smriti ii-67 it is stated as follows:
VaivAhiko Vidhih StriNAm SamskAro Vaidika: Smritah !
Pati SevA Gurau VAso GrhArtho AgniparikriyA !!
For girls the VivAha Vedic ceremony is to be done in lieu of Upanayana.
Their Serving the husband is in lieu of Gurukula VAsa.
Their Performance of household duties is in lieu of worship of sacrificial fires