Is it mutar for a girl who is under bas mitzvah to sign a man’s leg cast? What about a girl who is over bas mitzvah? They are not related to the man whose leg is in the cast.
In a formal sense, the prohibition of touching a member of the opposite sex applies only to such a touch that can be considered derech chibbah, meaning a way of touching that could create some degree of arousal between the two. Because of this condition, there has been a very broad debate over the permissibility or otherwise of shaking a woman’s hand. Although most poskim have prohibited this practice, some have opined that where the woman in question would be embarrased by the refusal to shake her hand, one may be lenient.
If there is no need for it, it is better to avoid contact between the sexes even when no derech chibbah is involved, because the line is not always easy to draw. Although signing a plaster cast (arm of leg) would not usually be a case of derech chibbah, it would therefore remain preferable for a girl not sign a male non-family-member’s cast. However, there is no need to be stringent for a girl beneath the age of bas mitzvah.
Sources: Concerning handshakes, see Iggros Moshe, Even Ha’ezer, vol. 1, no. 56: “Concerning that which you saw people being lenient, and even those who are God-fearing, to offer their hand to a woman when she stuck her hand
out — perhaps they reasoned that this is not derech chibbah and taavah, yet in practice this is difficult to rely on.” In Even Ha’ezer, vol. 4, no. 32 (9), he writes that it is prohibited to offer one’s hand to a woman (to shake), and adds that this cannot be compared with a bus journey, in which there is no chibbah at all. Rav Yaakov Kaminetzky (Emes Le’Yaakov on Tur and Shulchan Aruch, p. 405) writes that there might be room for leniency in places where the woman will be embarassed: “Regarding returning a handshake to women when they extend their hand first in greeting, not in an affectionate manner, this is a very serious question and it is difficult to be lenient. However, in circumstances where the woman may come to be embarrassed, perhaps one could consider being lenient. This requires further study.”
Signing a cast is perhaps less derech chibbah than a handshake, but is certainly not comparable to journeying on a bus. Because there is no issue of offending the cast-wearer, it would appear proper to avoid it, yet there would not be a need to be stringent for a girl beneath bas mitzvah.