Previous research suggests a curvilinear relationship between child disability and physical abuse, with children with mild impairments at greater risk than both children with severe impairments and superior functioning. Using a national probability sample of families investigated for maltreatment (N = 1675), this study tested for both linear and curvilinear relationships of child functioning to parental physical assault. Linear relationships were found between problem behaviors and minor and severe assault, and between social skills and minor assault: the more impaired the level of child functioning, the greater the risk. Curvilinear relationships were found in which children with mildly impaired or average language skills were at greater risk for minor assault than both children with severe impairment or above average and superior skills. Children with superior daily-living skills were at lower risk for severe assault than all other children. Implications for understanding processes underlying parental physical assault of children with impairments are discussed. (Published Abstract)