It doesn't appear that there is any reason he can't shape shift into other humans, albeit green ones.
Beast Boy has the ability to morph and transform into any animal that he has seen himself or has seen in an illustration (as is the case when he shapeshifts into an animal such as an extinct dinosaur) wikipedia
He also doesn't appear to be constrained by Earth-born creatures, or even by creatures with a certain lower limit of intelligence.
Beast Boy has also shown the ability more than once to transform into alien animals, including sentient species such as the Gordanians.wikipedia
He has total control of his shape shifting abilities.
Recently he has also shown the ability to partially transform into an animal, such as acquiring octopus tentacles on the lower half of his body, while his upper-torso remains unchanged.wikipedia
So either he can take the shape of other humans, and simply never has (or never has thought to try) or it is an arbitrary constraint imposed by the writers that makes no logical sense. Unless they don't consider humans to animals...
Now maybe, maybe, he can only take one form of a creature he morphs into. One version of a T-Rex, one version of a gorilla, one version of a mouse, and one version of a human.