West Yorkshire Police initially reported the trio had been trying to break into cash machines, but said this morning that their target had been car parking payment machines in the town.
The Force Command Hub had described on Twitter how officers were dispatched in the early hours when the men were spotted on CCTV cameras.
It said the suspects tried to run off but had been tracked by CCTV camera operators, who guided officers to their location.
A spokeswoman said: "Three men have been arrested on suspicion of theft in connection with thefts from car parking payment machines in Halifax.
"The men - aged 25, 26 and 37 - were arrested between 2.15am and 2.25am this morning in the vicinity of North Bridge Leisure Centre, Halifax. They remain in custody at this time."