You have the right no not answer the door for anyone, including the police. Be aware however, if they have a valid warrant, and you don't answer they may be able to forcibly enter your home. If you are under investigation for a criminal matter, remember do not talk to them except to assert your right to an attorney. Then get a criminal defense attorney ASAP. Best of luck.
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Just like anyone knocking on your door, they need your permission to enter. If they knock it down, they better have a warramt.
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Only you can decide if you should open the door. But you do have the right to deny them entry. If they have a warrant, they will come in whether you deny or not. If they don't have a warrant, they could get one. As a probationer or parolee, allowing entry without a warranty be a requirement that you agreed to. In that case, not allowing entry could be a violation, resulting in your going back to jail.
Contact a criminal defense attorney to determine what your rights are.