Safe Drinking Water Assistance Act of 2017 This bill addresses contaminants of emerging concern (emerging contaminants), which are not regulated under a national primary drinking water regulation and may have an adverse effect on human health. The Environmental Protection Agency (EPA) must review federal efforts to: (1) identify, monitor, and assist in the development of treatment methods for emerging contaminants; and (2) assist states in responding to the human health challenges posed by those contaminants. In addition, the EPA must establish a strategic plan for improving those efforts. The EPA and the Department of Health and Human Services must jointly establish an interagency working group to coordinate federal activities that identify and analyze the public health effects of emerging contaminants. The Office of Science and Technology Policy must establish a National Emerging Contaminant Research Initiative for developing an interagency federal research strategy that specifies and prioritizes the research necessary to improve the identification, analysis, monitoring, and treatment methods of emerging contaminants. Specified federal agencies must make grants for research proposals selected by the initiative as likely to result in significant progress toward achieving the strategy's objectives. The EPA must: (1) report on actions it may take to increase support for states that require testing facilities for emerging contaminants in drinking water samples; and (2) develop a program, based on the report's findings, to provide assistance to eligible states for the testing and analysis of emerging contaminants.