Interpol and the warrant clerk
Filing a warrant is a paperwork problem before it's a detective one, and the series dresses that paperwork up differently every time.
The player-facing fiction of the warrant mechanic is that ACME works through Interpol, the real-world international police organisation, to check a suspect's recorded traits against outstanding dossiers. The Deluxe remake of the original game makes this literal with an on-screen Official Interpol Map, used to see which countries hold live leads, while the actual matching work is handed to a character — Warren the Warrant Robot — rather than a faceless terminal.
Wanda, at the counter
In the series' voiced CD-ROM reissues, that clerical work gets a face and a voice: Wanda, the warrant clerk who processes what a player files. It's worth being precise about her, since fan memory of the role is patchy: there is no agent called Sally in these games; the clerk who signs off on a warrant is Wanda.
What “issued” actually means
Mechanically, obtaining a warrant is a gate, not a formality. Every version of the rule is stricter than it sounds: file a warrant against a name that doesn't match the crook eventually cornered, or arrive with no warrant at all, and the arrest simply doesn't happen. The 1985 manual's version of the warning is blunt — get it wrong and “you'll be thrown off the case!” — and every sequel keeps some version of that same hard stop. The paperwork isn't set dressing around the chase; it's a second win condition running in parallel with it.
Europe's Crime Lab computer adds a wrinkle worth knowing before submitting: editing recorded notes and re-entering them can void a warrant already on file, so a careless double-check late in a case can cost a filing that was already earned.