Chaotic neutral.
My impression from the film was that he will do anything to recover the girl because of his personal feelings for her. He did not act on any of the other kidnappings of innocents etc earlier in the movie, so he is not acting on some moral principle. He is certainly acting outside his contract, especially after he warned the father what level of performance to expect.
In the end he puts her life above his own, but I think neutral people can do that. Any alignment can value their family, for example, that highly. I believe it is a similar emotional meaning the girl has for him. Good people might do so for strangers - they consider people's value as absolute, not defined by their relationship to the person.
He does not 'give the law time to find her', he is out of commission for that time and begins the hunt as soon as he is able. Chaotic alignment does not mean someone's actions are random or they are unable to plan. He does not care for the local law forces - admittedly with reason - and we learn little about his personal moral code except that he believes he has done, and is doing, wrong. He does whatever he wants to do, which I think makes him Chaotic.
He is brutal and violent in the search, but does not seem to enjoy it, or be particularly over the top. For example after getting the info he wanted from the guy in the car he shoots him dead. He doesn't set fire to the car. Pain is a means and not an end. These actions are definitely on the evil side of neutral, but I don't think it's quite enough to make him Evil.
The chaotic/neutral and neutral/evil lines vary from campaign to campaign though, so I could understand putting him in any of those four boxes.