Background In Brazil, the transmission of Leishmania infantum in urban settings is closely related to infection among dogs, with occasional transmission to humans. Serological screening of dogs for Leishmania spp. infection on requests of their owners (passive case detection) represents a frequent, but little studied, practice within the scope of Brazilian public health. This study identified factors associated with canine visceral leishmaniasis (CVL) diagnosis-seeking behavior of dog owners in Rondonópolis (236,000 inhabitants), a municipality in Central-Western Brazil where VL is endemic. Also, we evaluated the profile of dog owners and their animals screened on free demand. Methodology/Principal findings Using mixed effects negative binomial regression, we modelled the number of dogs screened for Leishmania infection on free demand per neighborhood from 2011 to 2016 as a function of time-dependent predictors (current or recent canine seropositivity and human VL incidence), distance to the screening site, and demographic variables. We assessed potential delays in the effect of time-dependent predictors on the outcome. Among 12,536 dogs screened for Leishmania infection, 64.2% were tested during serosurveys and 35.8% were tested on free demand. Of these, 63.9% were positive. Uptake of screening under free demand was strongly associated with higher levels of canine seropositivity in the neighborhood (current or recent) and decreasing distance to the screening site. A subsample of dog owners (n = 93) who sought CVL screening between 2016 and 2017 were interviewed in more detail. Owners with better socioeconomic status and dogs with apparent CVL clinical manifestations prevailed among them. Conclusions/Significance To support timely CVL management, passive case detection along with awareness activities aimed at dog owners should be encouraged in endemic areas. Screening sites should be prioritized in accessible zones, as well as in socio-economically disadvantage areas. In parallel, CVL active case detection should be continued as a surveillance tool to guide control actions.