1) A Jew may not wash clothes for a non-Jew during the week of the ninth of Av (even according to the opinion of the Rem”a), because it looks like he is doing it for himself. If it is clear to everyone that they are clothes of a non-Jew, one may be lenient. Similarly, if he has no food to eat unless he continues his business of washing clothes for non-Jews, it is permitted. (Shulchan Aruch and Mishne Berurah 551)
2) It is forbidden for Jews to give clothes to a non-Jew to wash during this period, even if the actual washing will take place only after the end of these days. One may give the clothes before the beginning of this period, even if the actual washing will take place during these days. (Latter Authorities)