MB 17: Jointly-owned - And a talis which is jointly-owned by a Jew and a non-Jew or by a man and a woman IS obligated in tzitzis, but he should not bless on it. [Thus says the] Artzos HaHayyim, not like the Damesek Eliezer, see there.
MB 18: Is obligated - And this refers to the case where his partner is agreeable that he wear it and it is without tzitzis, then he is required to put tzitzis on it; but if it has tzitzis and one partner is particular that the other not wear it, then even if the talis is big enough that it could be divided in two and each half would have the minimum size required for a talis [and we could think of the big talis as being composed of two small ones], even so, if he wears it against his partner's wishes, it is like theft, and if he blesses on it, he trangresses the commandment of "Thou shalt not take the name of the L-rd thy G-d in vain," because the partner's half of the talis has two tzitzis which are not his, and all the more so if it does not yet have tzitzis [that he may not put on tzitzis and wear the garment and bless on it]. And according to this, a talis which is left as an inheritance from one's father and his brothers are particular about it [that he not wear it], he should be careful not to bless on it until they come to an agreement.