I assume intentional vandalism is a basically a crime. When the police will not investigate an incident but you know who did it and want to bring a cause of action to recover damages from the vandalism, how does one term that cause of action and what are the elements? It can be proven by the greater weight of circumstantial evidence.

If the property is "tangible personal property", like a bicycle, and not "real property", like land or structures attached to the land, then one cause of action might be Conversion listed in the class on plaintiff's right to sue. Other causes of action would arise from violation of law and damages resulting. You might just allege DAMAGE TO PROPERTY and allege (1) plaintiff owns the property, (2) defendant caused damage to property by *****, and (3) plaintiff suffered money damages as a proximate or direct result. Use discovery later to prove what the damages cost you, i.e., fair market value or loss of use, etc.