For Amusia

This study "investigated the impact of congenital amusia, a disorder of musical processing, on speech and song imitation in speakers of a tone language, Mandarin." Individuals with congenital amusia imitate pitches more accurately in singing than in speaking: Implications for music and language processing | SpringerLink :

Amusia — SYNC PROJECT : "there are individuals in whom the mechanisms function in a way that even normal processing of musical sounds is not possible...called tone-deafness or amusia, typically affecting around 4 % of the population."

Unfortunately, this article costs over $50, but it does address "the work that has been done concerning singing among nonmusicians, focusing on pitch accuracy, which is one of the most important aspects of singing." Will review it if we manage to get a copy. Perception and action in singing - ScienceDirect

This very detailed look at the brain as it processes pitch does not address amusia directly, but it may be of interest to amusiacs looking to learning more about how our brains handle music: Pitch Processing Sites in the Human Auditory Brain