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Background
While questioning Ruby during the task
Look for Ruby on the Coast, she'll claim that she's been hiding in the
Feld Building (#1) because of you, since you're with La Puta Madre. Of course, you won't know if this is true or not.
While you're reading
Ruby's Journal at the end of the task, you'll be able to look for references to La Puta Madre. You won't find anything obvious, but if you have 4 Logic, then you'll spot some places where Ruby talks about "M," including calling you "M's peone."
Finally, when you put away the journal, you'll be able to ask Kim for his opinion on the matter. He won't think you're with La Puta Madre, but he'll suggest calling your precinct and asking someone there. Kim's answer will trigger the task.
Walkthrough
You won't be able to call your precinct until after completing the task
Return to the Whirling-in-Rags (aka the mercenary tribunal). At that point, if Kim is still around, then you'll be able to use the radio in his car (#2) to call your precinct. If Kim isn't around, then his car will be gone, too, and you won't be able to complete the task.
When you call your precinct, Jules Pidieu, the officer on call, won't really answer your question, but he'll imply that you aren't with La Puta Madre. This will complete the task and earn you 10 xp.
1 - Feld Building
2 - Kim's Car