Assuming your map is drawn onto a WPF Canvas at the origin (0,0), that exists on the MainWindow of a new WPF project, what you could do is this:
1) In the codebehind file MainWindow.cs, create a Dictionary of "hitboxes" that define square regions on the map, and the relevant US state name.
2) Create an event handler for when the mouse moves over your Canvas. This event handler will give you the coordinates of the mouse.
3) Search the Dictionary to see which entry contains your current mouse coordinate, and retrieve the state name from the entry (if their is one).
This is pretty broad but without code examples of what you're trying to do it's at least a start.