The rules for this vary from state to state. However, even if it is not actually illegal, you could still be prohibited from using it against the person that you record.
The issue of recording phone conversation is a complicated one. Check out this link and the table of the various state laws: http://www. callcorder. com/phone-recording-law-america. htm
It is illegal to record phone conversations if you do not let the person know they're being recorded unless it's for a criminal investigation. Recording a person's phone conversations is a serious privacy issue. Usually wjen you call customer service, the operator tells you your calls may be monitored. If they don't say this, they're recording illegally.
In most states it is illegal to record phone conversations without informing the other party that the call is being recorded. Let's say that you record without telling the other person and you need it for evidence. The judge would not allow it to be used as evidence because you violated that person's civil right.
Each state has their own laws regarding this. some states you can record as long as both parties know others only one party has to know, that can be you.