SummaryBackgroundScotland's Baby Box Scheme (SBBS) is a national programme offering a box of essential items to all pregnant women in Scotland intended to improve infant and maternal health. We aimed to evaluate the effect of SBBS on selected infant and maternal health outcomes at population and subgroup levels (maternal age and area deprivation).MethodsOur complete-case, intention-to-treat evaluation used national health data (from the Scottish Morbidity Record [SMR] 01, SMR02, and the Child Health Surveillance Programme-Pre School), linking birth records to postnatal hospitalisation and universal health visitor records in Scotland. We considered maternal–infant pairs of all live-singleton births 2 years either side of SBBS introduction (Aug 17, 2015, to Aug 11, 2019). We estimated step-changes and trend-changes in outcomes (hospital admission and self-reported exclusive breastfeeding, tobacco smoke exposure, and infant sleeping position) by week of birth using segmented Poisson regression, adjusting for over-dispersion and seasonality where necessary.FindingsThe analysis comprised 182 122 maternal–infant pairs. The prevalence of tobacco smoke exposure reduced after SBBS introduction: step decrease of 10% (prevalence ratio 0·904 [95% CI 0·865–0·946]; absolute decrease of 1·6% 1 month post-introduction) for infants and 9% (0·905 [0·862–0·950]; absolute decrease of 1·9% 1 month post-introduction) for the primary carer. There was no evidence of changes in infant and maternal all-cause hospital admissions or infant sleeping position. Among mothers younger than 25 years, there was a 10% step-increase in breastfeeding prevalence (1·095 [1·004–1·195]; absolute increase of 2·2% 1 month post-introduction) at 10 days and 17% (1·174 [1·037–1·328]) at 6–8 weeks postnatal. Although associations were robust to most sensitivity analyses, for smoke exposure associations were only observed early in the postnatal period.InterpretationSBBS reduced infant and primary carer tobacco smoke exposure, and increased breastfeeding among young mothers in Scotland. However, absolute effects were small.FundingMedical Research Council, Scottish Government Chief Scientist Office, and National Records of Scotland.