I forgot to record closing the browser, so I added it under TestCleanup.
Here is what I changed in the CodedUI Test:
1) click + to expand the Additional test attributes region
2) Un-comment the TestCleanup method
3) add a line to close the browser: "this.map.UIMSNcomWindowsInterneWindow.Close();"
public void MyTestCleanup()
// To generate code for this test, select "Generate Code for Coded UI Test" from the shortcut menu and select one of the menu items.
// For more information on generated code, see http://go.microsoft.com/fwlink/?LinkId=179463