Although Petitte was a very good pitcher throughout his 16 year career, the numbers do not indicate an automatic trip to the Hall. The strongest case to be made in his favor is a record 19 postseason wins (all but one with the Yankees).
The strongest case against enshrinement: only 240 regular season wins, only 2 seasons of 20+ wins and no Cy Young Awards.
Sure, the postseason record is pretty amazing but consider he was also on some great Yankee teams. To me, that's as much an argument against as in favor of enshrinement.
I think it will be a close call once he's eligible for the Hall. A case can be made for enshrinement but I'm not sure his career matches up with those already in the Hall. If he had been able to pitch a couple of more years and rack up another 20-30 victories it would be more of a lock. In the end, I think Andy Petitte will be remembered as one of the best Yankee pitchers ever and a very good pitcher during his time. But I don't think he will be considered a great pitcher and just barely miss enshrinement into Cooperstown.