Not in the first instance they don't. I find it astonishing that their daughter disappears and they don't even go round to the police station at some point the next morning. You would think they were scared??
In fact it sounds awfully like a retake from the Leonor Cipriano case, she delayed contacting the police too!!
Technically, they did go round to the police station next morning, where next morning was 4 May 2007.
They got picked up by the PJ and were taken to the nearest PJ station, in Portimão, where they gave their first statements.
There is no police station in Luz, so they couldn't go to that.
The nearest GNR station is Lagos. I can't tell you for certain whereabouts it is in the town. But I doubt the GNR could have/would have given them an update.
The nearest PJ station is Portimão. I only know of that (from news reports) and where it is 'cos I have trawled through Streetview trying to find it.
I dare say a taxi plus driver would have done the trick, but this was still at the stage when the McCanns were trying to work out who/what the GNR were and ditto the PJ were. Calling a taxi and saying "take me to the nearest police station" would not have worked.