Under-five mortality is a survival measure that reflects the social, economic, and environmental conditions in which children live, including their health care, so they are reasonable measures to identify vulnerable populations. Infant Mortality, also a survival measure, refers to children dying before reaching the first year of life, and can also be disaggregated into events below 28 days, referred to as neonatal mortality, which currently concentrates the higher share of deaths. In 2020, more than 5 million under-five children died in the world, from which almost 50% occurred among newborns. The Sustainable Development Goals call for an end to preventable deaths of newborns and children under-five, but considering the current trends, many countries are not on track to achieve it. Neonatal mortality involves various biological, socioeconomic, and healthcare factors, and understanding its determinants can favor public policy funding planning and help with this problem. The increasing relevance of neonatal deaths aside from online platforms that make available health data in Brazil has enabled more precise analyses and led to a significant number of studies covering different factors, regions, and methods regarding this issue. Among the various determinants, access to private health services is an important one. In Brazil, mainly due to financial restrictions, a huge percentage of the population uses only public health services. In this context, the objective of this paper is to perform an evaluation of the NMR in the city of São Paulo - Brazil, in the period between 2012 and 2017, considering as a determinant for neonatal mortality rate if the delivery has occurred on private or on public health service sphere. Besides that, the determinant mother's age is also included in the analysis, so it is also possible to evaluate associations between these two variables. A dataset having 8,110 neonatal deaths was analyzed and three graphics were created. The first one is used to assess information regarding the distribution of births by health service sphere and mother's age. The second brings information on births and neonatal mortality rates combined and compared by year and by health service sphere. Finally, in the last one births and rates are also combined and compared by year, health service sphere, but now are desegregated by mother's age group. From these results, some insights are raised and discussed, and some need further investigation to obtain more conclusive results, but the currents can already bring important knowledge about the problem.