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