Neighbor taped this to my door

That means falsely alleging that a crime happened. Not calling and truthfully saying whatdid happen, even if there is no actual "crime".
If you call and "report" something, though, they know all that shit on subsequent calls (both for you and the person you are complaining about), they have it on record. If something is called to your name or address they will have that prior event at hand when they arrive, even if you were just being a good citizen on the prior incident. Been there. That can stand very much in your stead if you are in the right, either way oddly enough (i.e. prior legit-sounding complaints will be taken seriously, but if they have obviously malicious/spurious complaints form a particular complainant, and get another one, you better bet they will take that into account in responding too).

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