You may, possibly, qualify for a Stalking Protective Order. You can ask the court for a Stalking Protective Order against any person who has repeatedly (two or more times) had contact with you that made you fear for your safety, or the safety of a family member. That fear must be objectively reasonable, as determined by a judge.
To apply for such an order, you must submit a petition to the court, describing the conduct that justifies the restraining order. Your local courthouse has forms available for this purpose. A judge reviews the petition, and, if your description meets the requirements, signs the initial order. You must then have that order served upon the person being restrained (the respondent). You cannot do this yourself, but any other adult who lives in the state can do it. The county sheriff's office often performs this task, for a nominal fee (usually about $35). Once the order is served upon the respondent, it is effective immediately, and that person is prohibited by law from contacting you. The first violation is punishable as a class A misdemeanor; any subsequent violation is a class C felony.
Once the respondent is served with the order, they have the right to request a hearing. This is done by filing a form with the court, within 28 days of being served. The court must schedule a hearing within 14 days of the request. At this hearing, the person asking for the order (the petitioner) must show that the allegations in the petition are true. But they only must show this by a preponderance of the evidence - a greater than 50% chance.
A restraining order petition is a lawsuit, and entitles both sides to legal discovery and the right to counsel. You may be asked to produce evidence to demonstrate that your allegations are true, and that you really, and reasonably, felt threatened.
If this person is also your landlord, then there may be other remedies available to you as well. A landlord is not allowed to disconnect heat and electricity from a rental property if the tenant is up on their rent. But if you're moving soon anyway, then all of this may be more trouble than it's worth.
Restraining orders, in my experience, are often almost useless. The reason is this: You take out a restraining order against someone if you're afraid that they mean to do you harm. The order, if granted, makes it a crime for this person to be in contact with you. But if the person is really determined to do you harm, then this shouldn't deter them - harming you is already illegal, so if they really mean to do this, then they shouldn't be fazed by the idea that approaching you is illegal - they're already set on committing another, more serious crime! So restraining orders are useless against truly dangerous criminals. Rather, they have two major purposes: They make it possible to arrest someone a few minutes earlier into the commission of a crime. And, they send a general signal of social warning and disapproval. In my experience, this is what most people really seem to want when they file for such an order - they want a judge to shake their finger at the other person and say "You've been very bad!" But judges rarely do this, and it's a waste of the court's time to ask it.
I think you would be better served by a consultation with a landlord/tenant lawyer. They can tell you whether you have a cause of action against your landlord for rent you've paid, which might be more effective at halting abuses until you move.