A polícia vai investigar o roubo.

Because polícia is a feminine noun in Portuguese. Its grammatical gender is feminine, so it takes a.

That does not mean the police officers are female. Grammatical gender and real-world sex are separate things.

Also, a polícia usually means the police as an institution or force. If you mean a police officer, the most common word is o policial or a policial.

In Portuguese, a polícia is usually treated as a singular collective noun. So the verb is singular:

A polícia vai investigar...

English often treats the police as plural, but Portuguese does not usually do that with a polícia.

If you were talking about individual officers, you could use a plural noun, such as os policiais, and then the verb would be plural:

Os policiais vão investigar o roubo.

In normal sentences, a polícia is the standard form.

Leaving out the article, as in Polícia vai investigar o roubo, sounds more like:

• a news headline
• a label
• very compressed journalistic style

In everyday Brazilian Portuguese, the full sentence with the article is more natural: A polícia vai investigar o roubo.

Both are correct, but vai investigar is much more common in everyday Brazilian Portuguese.

• vai investigar = very common, natural, conversational
• investigará = correct, but more formal, more written, sometimes more official in tone

So this sentence sounds very natural in Brazil.

It is a near future construction:

• vai = present tense of ir
• investigar = infinitive

Literally, it is like is going to investigate, but in many cases it is simply the normal way to say will investigate in Brazilian Portuguese.

So: A polícia vai investigar o roubo
= The police will investigate the robbery

After ir used for the future, Portuguese uses the infinitive directly:

• vai investigar
• vou estudar
• vamos sair

English often uses to before the base verb, but Portuguese does not need a separate word here. The infinitive itself does the job.

So vai investigar is the normal structure, not something incomplete.

Because roubo is a masculine noun, and here it is being used with the definite article o, meaning the robbery.

This usually suggests a specific robbery, one that is already known from the context.

Compare:

• o roubo = the robbery
• um roubo = a robbery

These words can overlap in translation, but they are not exactly the same.

In Brazilian usage:

• roubo: robbery; in legal language, usually taking something through threat or violence
• furto: theft; taking without violence or direct confrontation
• assalto: holdup/robbery; very common in everyday speech for a violent robbery

So o roubo in this sentence is a natural way to refer to the robbery, especially in a general or official-sounding context.

Usually, for learners, it is best to think of a polícia as the police as an institution or force, not one officer.

For one officer, use:

• o policial = male police officer
• a policial = female police officer

That said, in informal Brazilian speech, you may sometimes hear ele é polícia, meaning he’s a cop or he works in the police. But that is more colloquial. For standard usage, policial is safer.

The accent shows the correct stress:
po-LÍ-ci-a

Without the accent, the stress would be expected elsewhere, so the word would be pronounced incorrectly.

This accent helps you know that the stressed syllable is lí.

Not exactly.

• A polícia vai investigar o roubo = the police will investigate the robbery
• A polícia está investigando o roubo = the police are investigating the robbery

So the first points to the future, while the second describes an action already in progress.

The normal order is:

subject + verb + object
A polícia + vai investigar + o roubo

This is the most natural order in ordinary speech and writing.

You can change the structure, but it changes the style or emphasis. For example:

• O roubo vai ser investigado pela polícia.
  Passive voice: The robbery will be investigated by the police.

That is also correct, but the original sentence is simpler and more direct.