At crime scenes, or something that appears to be a crime scene, either everyone will want to talk to the police, or no one will want to talk to the police. Either one can be equally challenging. At the "everyone" calls, some or most of the witnesses will be trying to spin the incident and mislead the officer. At the "no one" calls, at least one of the people present is likely to be the perpetrator, who will have intimidated the others into keeping quiet.
The officer is usually entering an unfamiliar environment, occupied by people who live, work, or visit there frequently. He will not know the hiding places or weapons stores that are well-know to the others there, some of whom may want to do him harm, or at least keep the evidence of their crimes secret to him.
Most calls do not result in arrests or other enforcement actions. The officer may only answer questions, give some advice, or take a report. He has to be able to sort out the true and relevant details from all the noise. It's one thing to be able to recite the elements of the major criminal statutes operable in his jurisdiction, but very much another to be able to apply a real-world situation to an assortment of hundreds of laws to decide if one or more of them has been violated.
As Allen Dean Benge pointed out, a crime is an act that has been proscribed by an appropriate governmental body. Crimes differ from other laws in that they include a penalty or range of penalties to be imposed on conviction. Statutes that define procedures or the licensing requirements for funeral directors aren't crimes, and comprise most of the statutes in a typical book of laws.
An "assault" case can differ from one place to another, depending on how the statutes are worded. An assault may include a battery, or may be just an attempt to commit a battery. Battery may require harm, or just be an unwanted touching. The officer investigating such a case has to reconcile the physical evidence and the statements of witnesses and make a decision on whether a crime occurred at all, if one occurred, which one, and whether he can or is obligated to make an arrest. In a domestic violence case, he may have the obligation to make an arrest if it's possible to do so. In other cases where he did not witness the crime, he may need to see if a victim or witness wants to sign a criminal complaint to enable an arrest.
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