In Texas, the charge is either Murder or Capital Murder.
At sentencing, the defendant can argue that it was a crime of passion which could lead to it being treated as a second degree felony.
Capital Murder has to have other aggravating items. These include killing a police officer or fireman, killing during a kidnapping, burglary, or sexual assault and so on.
What she did sounds more like 2nd degree murder or possibly manslaughter in my state. She certainly is guilty of homicide. Makes me wonder how she got to be a cop in the first place.