Population censuses are increasingly using administrative information and sampling as alternatives to collecting detailed data from individuals. Non-probability samples can also be an additional, relatively inexpensive data source, although they require special treatment. In this paper, we consider methods for integrating a non-representative volunteer sample into a population census survey, where the complementary probability sample is drawn from the rest of the population. We investigate two approaches to correcting non-probability sample selection bias: adjustment using propensity scores, which models participation in the voluntary sample, and doubly robust estimation, which has the property of persisting possible misspecification of the latter model. We combine the estimators of population parameters that correct the selection bias with the estimators based on a representative union of both samples. Our analysis shows that the availability of detailed auxiliary information simplifies the applied estimation procedures, which are efficient in the Lithuanian census survey. Our findings also reveal the biased nature of the non-probability sample. For instance, when estimating the proportions of professed religions, smaller religious communities exhibit a higher participation rate than other groups. The combination of estimators corrects such selection bias. Our methodology for combining the voluntary and probability samples can be applied to other sample surveys.