Put Trafficking Victims First Act of 2017 This bill directs the Office for Victims of Crime within the Department of Justice (DOJ) to publish a report on state safe harbor laws, including: (1) the impact of state safe harbor laws on victims of trafficking, and (2) best practices and recommendations on the development and implementation of effective state safe harbor laws. The bill amends the Victims of Trafficking and Violence Protection Act of 2000 to modify requirements with respect to the allocation of trafficking victim services grant funds for training and technical assistance. Specifically, it requires training and technical assistance to be provided in coordination with the Department of Health and Human Services. Additionally, it broadens the areas of training and technical assistance to include, among others, investigating, prosecuting, and preventing human trafficking through a trauma-informed and victim-centered approach. The National Institute of Justice must: establish a working group to identify and recommend best practices for collecting data on human trafficking; report on efforts to develop methodologies to determine the prevalence of human trafficking in the United States; and coordinate with federal, state, local, and tribal governments, and private organizations, to survey survivors to estimate the prevalence of human trafficking in the United States. DOJ must report on efforts to increase mandatory restitution orders and asset forfeiture to provide restitution to victims of trafficking. The bill encourages states to implement certain protections for victims of trafficking.