Unfortunately you cannot get either case off your record. Domestic violence assaults cannot be sealed even if they are deferred. The criminal trespass you could have sealed, but you lost the right when you picked up the assault case. Sorry to be the bearer of bad news.
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The best you can do is petition the court for nondisclosure (sealing) your trespass if you did receive deferred. You cannot do anything wiht the assault. Neither can be expunged.
Neither can be permanently removed or "expunged" from your record since they were neither outright dismissals or aquittals. However, contact an attorney to see if you can get them nondisclosed.
Unfortunately, Ms. Jaggers is correct. You dont qualify for expunction of either case. While you'd normally be at least eligible to ask for a nondisclosure of the criminal trespass, a family violence conviction or deferred adjudication probation will disqualify you from eligibility to get a nondisclosure order on ANY case. Sorry.