Accurate single cell mutational profiles can reveal genomic cell-to-cell heterogeneity. However, sequencing libraries suitable for genotyping require whole genome amplification, which introduces allelic bias and copy errors. The resulting data violates assumptions of variant callers developed for bulk sequencing. Thus, only dedicated models accounting for amplification bias and errors can provide accurate calls. We present ProSolo for calling single nucleotide variants from multiple displacement amplified (MDA) single cell DNA sequencing data. ProSolo probabilistically models a single cell jointly with a bulk sequencing sample and integrates all relevant MDA biases in a site-specific and scalable—because computationally efficient—manner. This achieves a higher accuracy in calling and genotyping single nucleotide variants in single cells in comparison to state-of-the-art tools and supports imputation of insufficiently covered genotypes, when downstream tools cannot handle missing data. Moreover, ProSolo implements the first approach to control the false discovery rate reliably and flexibly. ProSolo is implemented in an extendable framework, with code and usage at: https://github.com/prosolo/prosolo