From the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from romanrite.com/girm.html :
"317. In no way should all the other things prescribed by law concerning the reservation of the
Most Holy Eucharist be forgotten. [footnote 131: 131. Cf. particularly in Sacred Congregation for the Sacraments, Instruction Nullo umquam
tempore, 28 May 1938: AAS 30 (1938), pp. 198-207; Codex Iuris Canonici, cann. 934-944.]
This 1938 Instruction is at romanrite.com/nullo.html and includes:
“7. Special remarks must be made regarding the keeping of the key of the tabernacle in the churches of nuns or sisters, and in pious or religious houses of women. In view of the Statute of Canon 1267, whereby every privilege to the contrary being recalled, the Blessed Eucharist cannot be kept in a religious or pious house, except in the church or principal oratory, nor in the case of nuns, within the choir or enclosure of the monastery, local Ordinaries should bear well in mind, and insist on it, that the key of the Sacred Tabernacle is not to be kept within the enclosure. [Footnote 7: Cfr. Resolution of S.C.R., May 2, 1878, ad VI (decree 3448); H.E. Cardinal PETROUS GASPARRI, op. cit., 266, n. 998] Henceforth it is to be kept in the sacristy, so as to be obtainable at once, when need arises, and, when the church functions are over, and especially at night, it is to be placed in some safe, solid and secret receptacle under two keys, one of which is to be kept by the Mother Superior of the Community, personally or through a substitute, the other being entrusted to some nun, for instance, the sacristan, so that the offices of both are required in order to unlock the above-said place. Let their Lordships, the Bishops, give due attention to this ordinance, and rigidly insist on its execution, without any acceptation of persons, so that abuses and irreverences be avoided, which redound on the Blessed Eucharist.”
The previous paragraph had: “… If he leaves the key in the sacristy under another key; he can give this latter to the sacristan during such time as he is absent, and the key of the tabernacle may be needed. …” Presumably this was referring to a male sacristan.
So what has changed since 1938? Females can become Extraordinary Ministers of Holy Communion. In this role: “Such ministers may open the tabernacle and also, as required, place the ciborium on the altar or place the host in the monstrance. At the end of the period of adoration, they replace the blessed sacrament in the tabernacle. …” (Holy Communion and the Worship of the Eucharist Outside of Mass, n. 91, from The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0, page 673).
Also the 1983 Code of Canon Law has in 938 “The person in charge of a church or oratory is to see to it that the key of the tabernacle in which the blessed Eucharist is reserved, is in maximum safe keeping.” But it does not say the key must be held be a cleric, or that a male sacristan is safer than a female one. These assessments are to be made by the person in charge.