A polícia continua a investigação.

That a is the feminine singular definite article, meaning the.

So:

• a polícia = the police

In Portuguese, definite articles are used more often than in English, so A polícia is the normal full way to say the police in a sentence like this.

In Portuguese, polícia is grammatically singular when it refers to the police as an institution or force.

That is why the verb is singular too:

• A polícia continua... = The police continue / is continuing...

English treats police like a plural-looking word, but Portuguese treats polícia as a singular noun here.

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

• Os policiais continuam a investigação. = The police officers continue the investigation.

Continua is the third-person singular present indicative form of continuar.

So it matches the singular subject a polícia:

• eu continuo = I continue
• você / ele / ela / a polícia continua = you / he / she / the police continues

In English, this present tense can be translated in more than one way depending on context:

• continues
• is continuing
• sometimes even keeps on with

It can mean either one, depending on context.

Portuguese present tense often covers both:

• a simple present idea: continues
• an ongoing action idea: is continuing

So A polícia continua a investigação could naturally be understood as:

• The police continue the investigation
• The police are continuing the investigation

English chooses between those more strictly than Portuguese does.

Here, the second a is also the definite article the.

So the sentence breaks down like this:

• A polícia = the police
• continua = continues / is continuing
• a investigação = the investigation

That means investigação is the direct object of continua.

So this is not:

• continua a investigar = continues to investigate

Instead, it is:

• continua a investigação = continues the investigation

Because a investigação means the investigation — a specific investigation that is already known from the context.

This is very common in news and formal reporting, where the listener or reader already knows which investigation is being discussed.

Compare:

• a investigação = the investigation
• uma investigação = an investigation

So this sentence suggests a particular investigation, not just any investigation.

Yes. In Brazilian Portuguese, that is very natural.

These are all possible, with slightly different structures:

• A polícia continua a investigação.
• A polícia continua investigando.
• A polícia continua a investigar.

Notes:

• continua a investigação sounds a bit more formal and noun-based, like news or official language
• continua investigando is very natural in Brazil
• continua a investigar is grammatical, but this a + infinitive pattern is more associated with European Portuguese or with more formal wording

So for Brazil, A polícia continua investigando is a very useful alternative to know.

Because both nouns are grammatically feminine:

• a polícia
• a investigação

This is grammatical gender, not biological gender. It does not mean the police or the investigation is female in a real-world sense.

The article has to agree with the noun:

• feminine singular nouns take a
• masculine singular nouns take o

For example:

• a polícia
• o policial = the police officer

Usually a polícia refers to the police as an institution, force, or authority.

So in this sentence, it sounds like an official or institutional subject:

• A polícia continua a investigação.

If you want to emphasize the individual officers, Portuguese often uses:

• os policiais

So the difference is roughly:

• a polícia = the police force / the police institution
• os policiais = the police officers

In normal full sentences, you would usually keep the article:

• A polícia continua a investigação.

Without the article, it sounds like a headline, caption, or very telegraphic style:

• Polícia continua investigação
• Polícia investiga caso

That kind of article-dropping is common in journalism, but not in ordinary complete speech.

A rough pronunciation guide is:

• A polícia ≈ ah poh-LEE-see-ah
• continua ≈ kohn-chee-NOO-ah
• a investigação ≈ ah in-ves-chee-gah-SOWN

A few stress points:

• polícia stresses lí
• continua stresses nu
• investigação stresses the final ção

The ending -ção is very common in Portuguese and is usually pronounced something like sown with a nasal sound.