While many of the liars gave convincing verbal accounts to the agents, when their drawings were compared with those of truth-tellers, there were features that distinguished them (Applied Cognitive Psychology, DOI: 10.1002/acp.1627).The technique isn't perfect, but as a supplement to existing interrogation techniques, it seems pretty useful. (And anything's got to be better than a polygraph.)
The first was who they drew: 2 out of 16 liars included the first agent in their drawing, whereas 12 out of 15 of the truth-tellers included that detail. Vrij suggests this is because the liars visualised a place they knew and simply drew this, neglecting to include the agent.
The second difference was perspective, with liars tending to draw the laptop handover from a bird's-eye perspective rather than a first-person one. Vrij suggests that while liars are adept at quickly coming up with a plausible verbal account, they find imagining spatial relationships between conjured-up objects more difficult from a first person perspective.
Of course, you can arrest veryone who asks if they can just draw stick figures. They're bound to be guilty of something.