People with really short hair can get a perm. However, if the hair is cut into layers, a perm should be avoided. Perms make short-layered hair frizzy and dry, which makes styling it difficult.
People with normal-length short hair are good perm candidates unless they have really fine hair. Perms are not recommended for baby-fine hair, as they contain ingredients that are harsh on delicate hair. People with naturally curly hair benefit from perms, because they relax the tight curls and make styling a lot easier.
People with naturally straight hair should consult with a professional hairstylist to determine if a perm is a good choice.