Instructions
Check for sexual organs. Obviously, this is easier done on a dead squirrel or a supremely tame one, but this is the only certain method of discrimination for most species of tree squirrel. The scrotum of male squirrels may even be obvious from a distance; a nursing female squirrel may exhibit prominent teats.
Identify sexually dimorphic characteristics if they exist. These are physical features common to but varying between the genders. Most tree squirrels are not sexually dimorphic. However, there are a few slight exceptions. The males of the African pygmy squirrel --- the most diminutive variety on the planet --- are slightly heftier than the females, so especially if several adults of these squirrels are seen together, you might infer that a comparatively larger individual is male.
Watch for behavioral cues. In several species of squirrels, as in the red-bellied squirrel of east Asia, multiple males actively contend for the attention of a single female during the breeding season. So if you see several squirrels squabbling over another, the tussling ones are likely male. Many species, like red squirrels, chase each other in courtship ritual, but the roles may shift, complicating gender discrimination.
Observe a tree squirrel tending to young in a nest. In some species, like Douglas squirrels (also called chickarees), male tree squirrels seem to assist in the construction of a maternity nest --- often built with leaves and twigs --- but do not actively care for the offspring once born. Thus, an adult squirrel carrying an infant in its mouth or exhibiting other such parental behavior is probably a female.