Genetic perturbation screens have the potential to dissect a wide range of cellular phenotypes. Such screens have historically been difficult in diploid mammalian cells. The recent derivation of haploid embryonic stem cells provides an opportunity to cause loss of function mutants with a random mutagen in a mammalian cell with a normal genetic background. We describe an approach to genetic screens that exploits the highly active piggyBac transposon in haploid mammalian cells. As an example of haploid transposon (HTP) screening, we apply this approach to identifying determinants of cancer drug toxicity and resistance. In a screen for 6-thioguanine resistance we recovered components of the DNA mismatch repair pathway, a known requirement for toxicity. In a further screen for resistance to the clinical poly(ADP-ribose) polymerase (PARP) inhibitor olaparib we recovered multiple Parp1 mutants. Our results show that olaparib toxicity to normal cells is mediated predominantly via Parp1, and suggest that the clinical side effects of olaparib may be on target. The transposon mutant libraries are stable and can be readily reused to screen other drugs. The screening protocol described has several advantages over other methods such as RNA interference: it is rapid and low cost, and mutations can be easily reverted to establish causality.