La policía investiga el asesinato.

In Spanish, la policía is often treated as a singular collective noun when it means the police force or police institution.

So Spanish says:

• La policía investiga... = literally The police force investigates...

That is why the verb is also singular: investiga, not investigan.

If you wanted to talk about individual officers, you could say:

• Los policías investigan el asesinato.

That would match English the police more closely in grammar, because it is plural.

It can mean both, depending on the article and context.

• la policía = the police force / the police
• un policía = a male police officer
• una policía = a female police officer
• los policías = police officers

In La policía investiga el asesinato, it means the police as an institution, not one officer.

Investiga is the third-person singular present indicative form of investigar.

So it agrees with la policía, which is singular:

• la policía → investiga

If the subject were plural, the verb would change:

• los policías investigan

In Spanish, the simple present is very commonly used for actions happening now, especially in:

• news reports
• headlines
• formal statements
• general factual descriptions

So La policía investiga el asesinato can naturally mean:

• The police are investigating the murder

even though the verb is grammatically a simple present form.

This is very normal in Spanish.

Yes. That is also correct.

The difference is mainly one of style and emphasis:

• La policía investiga el asesinato = neutral, concise, very common in news style
• La policía está investigando el asesinato = emphasizes the action is in progress right now

Both are natural, but the simple present is especially common in short factual statements.

Because el asesinato is a thing/event, not a person.

In Spanish, the personal a is usually used before a specific human direct object:

• La policía investiga al sospechoso.
  The police investigate the suspect.

But with things, events, or abstract nouns, you normally do not use that a:

• La policía investiga el asesinato.

So here, no a is needed.

El asesinato refers to a specific murder, one that is already known from the context.

Spanish often uses the definite article when talking about something identifiable in the situation:

• el asesinato = the murder

If you said un asesinato, it would sound more like:

• a murder, one murder among others, not yet identified as a specific case

In a sentence like this, especially in a news-style context, el asesinato is the most natural choice.

The accent mark shows where the stress goes: po-li-CÍ-a.

It also helps show that í-a is pronounced in separate syllables.

So:

• policía = po-li-cí-a

Without the accent, the pronunciation rules would suggest a different stress pattern.

For learners, the important thing is simply to remember that the stressed syllable is cí.

The sentence uses the most neutral and standard word order:

• Subject + verb + object
• La policía + investiga + el asesinato

Spanish word order is somewhat flexible, but changing it usually changes the emphasis.

For example:

• La policía investiga el asesinato. = neutral
• El asesinato lo investiga la policía. = more emphasis on the murder

So the original sentence is the most straightforward version.

Both relate to killing, but they are not exactly the same.

• asesinato = murder
• homicidio = homicide / killing of one person

In general, asesinato suggests murder, often with intent or under specific serious circumstances. Homicidio is broader and more legal/technical.

So in everyday language:

• asesinato is the more natural word for murder
• homicidio sounds more legal or formal

In this sentence, asesinato is the natural everyday choice for murder.