In the first chapter, Rule 13, the Talmud Tractate SOFRIM stipulates that, among various other people, a woman cannot become a scribe (Soferet). The Gemara states:
This is the rule: Whoever cannot act in religious matters on behalf of the public is not permitted to write a scroll of the Torah.
The Vilna Gaon (GRA) commentates: Everyone who writes it must be a person who may act on behalf of the public in discharching a religious obligation.
A Gemara in Talmud Gittin 45b states the same but also adds Tefillin and Mezuzot. Thus, among various other people, a Jewish woman cannot act as a scribe for a Sefer Torah, a Mezuzah or Tefillin. One reason is that a woman is not obligated to put on Tefillin but a Jewish man is. Only one who is obligated can act as a Sofer.
Fine with me, as I am not planning to become a scribe. As a matter of fact, this would drive me crazy writing or drawing all these letters in a special way. 🙂