ASP.Net: Do I need to add javascript source of _ValidationScriptsPartial.cshtml to _layout.cshtml?

Partial Views are meant to be used inside other views. You would not normally add the validation scripts to the _layout.cshtml since that (_layout.cshtm) is used on every page.

However, if you have a view where you need to use these scripts you just add the partial view inside the .cshtml file of your view like this:

@section Scripts {
    @{await Html.RenderPartialAsync("_ValidationScriptsPartial"); }
}

If you created a standard web project with identity using VS 2015 then you can see an example of this usage in Views/Account/Register.cshtml