Does halakhah permit a woman to affix a mezuzah?
The Sefer Yeshouas Malkoi (פ''ה מהלכות מזוזה הלכה י) says She may not put up a Mezuzah. He brings a proof from a Gemara(מנחות מ''ב) that says a gentile can not sew, or work out the leather of the Tefillin as he may not write a Mezuzah so to he may not do the other jobs, therfore a women because they too can not write can also not put up a Mezuzah.
The Chasam Sofer in his SH"UT(יור''ד סימן רע''א ד''ה ולדידי) disagrees and says she may put up a Mezuzah and that Gemara is only talking about the production aspect the things that are learnt out of you shall write them but not the putting up of the Mezuzah as it is a side matter.
The SH"UT Eretz Tzvi(חלק א' סימן ט''ו) brings another point it would not make sense that you can make a Shliach to do somthing you yourself can not do.Known as
The Halacha is as the Chasam Sofer and it says in SHU"T Shevet Halevi (חלק ב' סימן קנ''ח ד''ה ג' ודע) who says it is allowed based on the fact that it can not be she can make a Shliach for somthing and can not do it herself.