Darkly, Madly Duology Series by Trisha Wolfe

The Darkly, Madly Duet is a dark psychological romantic thriller following the intense, twisted relationship between a brilliant criminal psychologist and her serial killer patient. 

Total 2 books in the series - 

• Born, Darkly (Book 1)
  Renowned criminal psychologist Dr. London Noble takes on one final patient to fulfill a contract: Grayson Pierce Sullivan, a convicted serial killer known as "The Angel of Maine". Grayson is not a typical killer; he acts as a vigilante, targeting those he believes have escaped justice.
• Born, Madly (Book 2)
  The conclusion picks up with Grayson's escape and the pair's descent into further madness as they move from doctor and patient to partners in a "violent dance"