Moed Katan, Chapter 3, Mishnah 2. This mishnah parallels the previous one in both structure and content: there the mishnah listed the people who are permitted to cut their hair on Chol HaMoed, and here it lists those who are permitted to launder their clothes on Chol HaMoed.
These are the ones permitted to launder their clothes on Chol HaMoed:
"HaBa MiMedinas HaYam" - one who has returned from a journey overseas, whether he arrived back just before Yom Tov or during Chol HaMoed itself.
"UMiBeis HaShivyah" - one who had been held captive by non-Jews.
"VeHaYotzei MiBeis HaAsurim" - one released from prison, and even from a Jewish prison.
"VeHaMenudeh SheHitiru Lo Chachamim" - one who had been placed under a ban, and the Sages lifted his ban during Chol HaMoed.
"VeChein Mi SheNish'al LeChacham VeHutar" - one who had vowed not to launder his clothes, and came before a Sage who released him from his vow during Chol HaMoed.
From here the mishnah goes on to list items that anyone may launder on Chol HaMoed:
"Mitpechos HaYadayim" - hand towels, which become soiled constantly. Even though they were laundered before the festival in honor of Yom Tov, they are laundered again on Chol HaMoed.
"Mitpechos HaSaparim" - the protective covering worn during a haircut, much like the cape a barber uses today. Those people who were permitted to cut their hair on Chol HaMoed also needed to have this covering laundered.
"UMitpechos HaSefog" - towels used for drying the body.
The same applies to the garments of zavim and zavos, niddos and women who have given birth. Two reasons are given: either because their garments become soiled more readily, or because they are about to begin the process of purification and need a change of clothing, and therefore they were permitted to launder on Chol HaMoed.
And likewise anyone moving from a state of tumah to a state of taharah, such as one who had been a metzora or was tamei from contact with a corpse, who wishes to launder the clothes that became tamei, is permitted to launder them on Chol HaMoed.
In summary: the mishnah listed those permitted to launder on Chol HaMoed - one returning from overseas, from captivity or from prison, one whose ban was lifted by the Sages, and one whose vow was released; the items that anyone may launder - hand towels, barbers' cloths and drying towels; and zavim, zavos, niddos, women who have given birth, and anyone moving from tumah to taharah. But for anyone else, laundering clothes on Chol HaMoed is forbidden.