What can I do if I have a massive personal problem with a future student?

the nature of the problem is that the student violently assaulted my girlfriend [...] Charges were filed and I stand by the seriousness of the accusation.

The fact that there is a criminal case involved makes this situation much more serious than just disliking someone. It doesn't matter whether you think you could behave impartially or not, the appearance of a conflict of interest is what is important, and that is most certainly present here. If the student is doing poorly, the student could accuse you of unfair treatment regardless of your behavior, and there would most likely be an investigation. It's better to avoid that possibility entirely.

You need to talk to your professor immediately. Depending on the status of the case, tell your professor that your girlfriend and the student are on opposite sides of a criminal case. This should convey the seriousness of the conflict without disclosing too many personal details. Keep in mind that there are privacy issues with saying too much about your student's personal life, in particular when it comes to criminal charges.

Work with your professor to figure out what the best solution is, whether that means switching sections with another TA, switching the student to another section, or putting in place defined procedures to prevent bias on your part (such as anonymous grading). It may be a good idea for your professor to involve an ethics adviser from the university, since the conflict of interest is so clear. Regardless of the outcome, by officially reporting this potential issue ahead of time, this will reflect positively on you in the event that the student does make any complaints.

As mentioned by other answers, the first thing you absolutely must do is speak with your professor about this.

However, you also asked for options to present to your professor. These options depend on exactly how much you feel you will be able to do fairly. For example, if you feel you will be unable to interact with this student in a fair and appropriate manner (which, by the way, is understandable), you may need to recuse yourself entirely from your current position (as you'd be unable to do any of the required responsibilities).

Here are a few options, however, which may help avoid a complete recusal:

• Anonymous grading. This will only work if you believe you can act appropriately in regards to the other responsibilities required. And, of course, your professor's willingness/ability to implement this. Keep in mind that such a system is often not trivial (it depends heavily on the subject matter, etc.). If all assignments are handed in on paper, perhaps suggest that each student uses their university ID number. I had a class where we all chose monikers (which we reported only to the professor) to use throughout the year to use on assignments.

• Ask for or supply your own co-instructor. Keep in mind that this should NOT be a friend of yours who could similarly be biased, nor at any time should you inform the co-instructor of the circumstances. Your professor may not be interested in paying for two instructors for one section, but perhaps you could work something out with another lab instructor to split the pay 75/25 (or something similar) for the hours required, as s/he will not actually be required to do anything.

• Your university undoubtedly has a legal/HR department to whom you can speak about this. I highly recommend checking in with them, as they would potentially be more likely to step in and swap your teaching times with another lab instructor without simply letting you go (as the professor may be wont to do).

• Through a mediator, ask the student to switch to a different section. As you noted, it's important to recognize that as much as the student in question is the scumbag, you're the one with the conflict of interest here. As such, should he choose to refuse, it's ultimately your responsibility to resolve the situation.

Kudos to you for recognizing such a situation and taking the appropriate steps to avoid it. I think many would have a harder time not punishing the student for his behavior while feigning innocence.

Update:

With the edit of the OPs Question I have to update my answer as the content of that edit changes the situation completely.

There only option you have here is to contact the appropriate staff (most likely HR) Get your conflict of interest documents taken care of and to work out with HR what you should do next.

The fact that there is a legal situation already in play make it that much more important to get the COI documents taken care of.