事故 and 事件: accidents and incidents
Distinguish accidents from notable incidents without prematurely assuming that a crime occurred.
An unintended accident
事故 is read じこ and refers to an unintended accident, such as a collision, injury, or equipment mishap. 「交差点で交通事故がありました」 says that there was a traffic accident at the intersection.
「事故の原因は調査中です」 says that the cause of the accident is under investigation. Do not add that a particular person's fault or intent has been established.
A notable incident
事件 is read じけん and refers to a notable occurrence or an incident under discussion or investigation. 「事件について話を聞きました」 means that the speaker heard about the incident.
Although common in crime reporting, 事件 does not establish that every incident is a crime. It can also be used in an exaggerated personal expression such as 「大事件」.
Information the label does not establish
「事故か事件か、まだ分かりません」 says that it is not yet known whether this was an accident or an incident of another kind. In this contrast, context may concern whether it was accidental or involved other circumstances.
Do not equate 事故 with an absence of negligence or 事件 with proven intent. Separate naming an occurrence from establishing its cause, responsibility, or intent.
Does 「事件を調べています」 mean that a culprit has already been found?
Show the answer and why
No. It describes an ongoing investigation into an incident. The sentence does not give the incident's nature or the investigation's outcome.

