How do investigative reporters prove their identity to the police? I'm writing a book and don't want any mistakes on how their jobs work so anything will be nice.

Journalists work for news outlets.

Accredited journalists work for the bigger brandname news outlets. The outlets (as well as the journalists’ trade unions) provide official credentials to their journalists, usually in the form of official credential letters, a journalists’ trade-union membership ID card, press cards, etc, indicating the particular journalist’s name, news organisation, department and job position.

Investigative reporters and certain types of correspondents (e.g. “White House Editor,” “Defence Editor,” “Diplomatic Correspondent,” “Foreign Correspondent”) are invariably accredited journalists. In some countries, the authorities issue official press ID cards to these journalists after the news organisations have registered them with the authorities.

In some countries, the authorities also assign (“embed”) a government official to accompany the accredited journalist to help “liaise” (i.e. monitor and censor) the journalist’s coverage work.

Example (me):—

Decades ago, I was a financial journalist. I had official credentials and press card from the publication I was working for and from the authorities, plus entry passes from the stock and commodity exchanges and regulatory agencies.

When I became a travel writer for a travel magazine, all I got was a company staff ID card and an official company employment letter stating explicitly I was a “Travel Writer” covering travel matters for sales and marketing purposes for a commercial lifestyle magazine and not a “journalist” and not doing news journalism. So I clearly couldn’t have had a press card because that would be an obvious contradiction in terms.