If there are not enough deacons, priests and instituted lectors then it is OK for a women to read part of the Gospel for the Passion.
According to the Roman Missal for Passion Sunday:
“The passion is read by the deacon or, if there is no deacon, by the priest. It may also be read by lay readers, with the part of Christ, if possible, reserved to the priest”. (From
The Roman Missal, Catholic Book Publishing Co., New York, 1985, pages 126.)
The 2002 General Instruction of the Roman Missal (GIRM) seems consistent with this:
“109. If there are several persons present who are able to exercise the same ministry, nothing forbids their distributing among themselves and performing different parts of the same ministry or duty. For example, one deacon may be assigned to take the sung parts, another to serve at the altar; if there are several readings, it is well to distribute them among a number of lectors. The same applies for the other ministries. But it is not at all appropriate that several persons divide a single element of the celebration among themselves, e.g., that the same reading be proclaimed by two lectors, one after the other, except as far as the Passion of the Lord is concerned.”
Women cannot be instituted lectors. According to 2002 GIRM “101. In the absence of an instituted lector, other laypersons may be commissioned to proclaim the readings from Sacred Scripture. …”.
So I think ideally there should be four deacons. If there were one priest, one deacon and two instituted lectors then a women should not be considered for the reading of the Passion Gospel.