Wasting police time is what your actor sets out to do, and is a crime in many jurisdictions.
New Zealand defines your exact plan as a crime, under section 24 of the Summary Offences Act:
[A person can be penalised if that person]
(b) with the intention of causing wasteful deployment, or of diverting deployment, of Police personnel or resources, or being reckless as to that result,
(ii) behaves in a manner that is likely to give rise to [serious apprehension for his own safety or the safety of any person or property, as described in part (i)], knowing that such apprehension would be groundless.
Hong Kong similarly makes this a criminal offence, in section 91 of the Criminal Procedure Ordinance:
(2) If a person causes any wasteful employment of the police by knowingly making to any person a false report tending to show that an offence has been committed, or to give rise to apprehension for the safety of any person or property, or tending to show that he has information material to any police inquiry he shall be guilty of an offence [and faces penalties described].
Likely the basis of both of the above, the United Kingdom makes it an offence in section 5 of the Criminal Law Act:
(2) Where a person causes any wasteful employment of the police by knowingly making to any person a false report tending to show that an offence has been committed, or to give rise to apprehension for the safety of any persons or property, or tending to show that he has information material to any police inquiry, he shall be liable on summary conviction to [penalties described].
But this is not restricted to Commonwealth or common law countries either. Germany has section 145d of the Criminal Code:
(1) Whosoever intentionally and knowingly misleads a public authority or an agency competent to receive criminal complaints about the fact
that an unlawful act has been committed; or
that the commission of one of the unlawful acts under section 126 (1) is imminent,
shall be liable to [penalties described]
(2) Whosoever intentionally and knowingly attempts to mislead one of the authorities indicated in subsection (1) above about the participants
in an unlawful act; or
in an imminent unlawful act under section 126 (1)
shall incur the same penalty.
On a related note, if done to create suspicion of others but not one's self, Canada calls this activity public mischief, and criminalises it in section 140 of the Criminal Code:
Every one commits public mischief who, with intent to mislead, causes a peace officer to enter on or continue an investigation by
(b) doing anything intended to cause some other person to be suspected of having committed an offence that the other person has not committed, or to divert suspicion from himself;