Section 281 of the Criminal Procedure Act 1986 (NSW) does not apply to admissions made by a person who voluntarily attends a police station and reports an incident, at least until the person has said something that provides grounds for the police officer to reasonably suspect the person has committed an offence. A person stating they wish to 'report a disturbance' does not, without more, make them a person who 'could reasonably have been suspected' of having committed an offence. The word 'reasonably' in s 281(1)(a) requires that something has been said or done providing some grounds for suspicion; a mere possibility is insufficient.
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