Accumulating research document the needs of intervention towards mental health problems in early childhood. The general child health surveillance offers opportunities for early detection of mental health vulnerability, conditioned the availability of feasible and validated measures. The Copenhagen Infant Mental Health Questionnaire, CIMHQ, was developed to be feasible for community health nurses and comprehensive regarding the range of mental health problems seen in infancy. Previous testing of the CIMHQ has documented feasibility and face validity. The aim was to investigate the construct validity of the general population measure by using the Rasch measurement models, and to explore the differential functioning of the CIMHQ relative to a number of characteristics of the infants, local independence of items, and possible latent classes of infants. CIMHQ was tested in 2,973 infants from the general population, aged 9-10 months. The infants were assessed by community health nurses at home visits, in the period from March 2011 to December 2013. Rasch measurement models were used to investigate the construct validity of the CIMHQ. Analyses showed an overall construct valid scale of mental health problems, consisting of seven valid subscales of specific problems concerning eating, sleep, emotional reactions, attention, motor activity, communication, and language, respectively. The CIMHQ fitted a graphical loglinear Rasch model without differential item function. Analyses of local homogeneity identified two latent classes of infants. A simple model with almost no local dependency between items is proposed for infants with few problems, whereas a more complicated model characterizes infants with more problems. The measure CIMHQ differentiates between infants from the general population with few and more mental health problems, and between subgroups of problems that potentially can be targets of preventive intervention.