Is this extortion or black mail?

I have received at least four e-mails from someone (I suspect my soon to be ex) who is threatening to slander me in order to force me to drop charges against them. Basically the e-mails state that if I don't drop the charges then "they" will go to my higher ups and have them conduct an investigation against me in order to destroy me and my career. Should I go to the feds or the local police?