The introduction of the accurate and procedurally easy non-invasive prenatal test (NIPT) raises ethical concerns that public attitudes towards prenatal screening may change, leading to societal pressure to participate in aneuploidy screening. This study examined Dutch citizens’ attitudes towards a pregnant woman’s decision to (1) decline NIPT in the context of two different funding policies and (2) to terminate or continue a pregnancy affected by different disorders. The attitudes of 1096 respondents were assessed with the contrastive vignette method, using two pairs of vignettes about declining NIPT and termination of pregnancy. Most respondents either agreed with a woman’s decision to decline NIPT or were neutral about it, stating that this decision should be made independently by women, and does not warrant judgement by others. Interestingly, funding policies did influence respondents’ attitudes: significantly more respondents disagreed with declining NIPT when it was fully reimbursed. Respondents had similar attitudes to the vignettes on termination and continuation of pregnancy in case of Down’s syndrome. In case of Edwards’ or Patau’s syndrome, however, significantly more respondents disagreed with continuation, citing the severity of the disorder and the child’s best interests. This study demonstrates broad acknowledgement of women’s freedom of choice in Dutch society; a finding that may help to rebut existing concerns about societal pressure for pregnant women to participate in prenatal screening. As the reimbursement policy and the scope of NIPT may influence people’s attitudes and elicit moral judgements, however, maintaining freedom of choice warrants sustained efforts by health professionals and policy makers.