A home that has a joint ownership:
It makes no difference how many Jewish partners there are in the ownership or rent of the home, either way it is obligated to have a Mezuzah. However if one of the owners or renters is a non-Jew, then it is exempt from having a Mezuzah.
 Michaber ibid
 Rama ibid
The reason: The reason for this is because 1) Part of it is owned by a non-Jew and is thus exempt from having a Mezuzah. 2) It may be dangerous, as the Non-Jew may suspect that the Jew is doing witchcraft on him. [Shach 286/6] 3) We learn that partners are also obligated in Mezuzah from the words “To increase your days” which is not applicable to non-Jews being that they do not fulfill the Torah, and thus are not deserving of long days. [Taz 286/2] The Shach ibid negates this latter reason.