We’re told that the six-year hiatus between “Rush Hour 2” and this latest installment in the Jackie Chan-Chris Tucker series of action comedies resulted from script problems. On the evidence of “Rush Hour 3,” the makers resolved the impasse in the simplest possible fashion—just do without a script of any consequence at all. String together some improvised comic riffs by Tucker’s garrulous policeman Carter (most culturally insensitive in the extreme, as well as coarse and puerile), a bunch of intervening action scenes for Chan’s Hong Kong detective Lee (all configured for his aging though still reasonably agile frame), and periodic jokey arguments and set-pieces involving the two (all of remarkable dumbness—e.g., a dopey reworking of Abbott and Costello’s “Who’s on First?” routine and a silly musical number), and that will be enough. Of course, there has to be some rationale behind it all—in this case, the search for a list of the leaders of the fearsome Chinese triad—and a revelation that will slow down the heroes’ progress—here, the fact that one of the chief villains is an old mate of Lee’s (Hiroyuki Sanada) whom he can’t bring himself to kill. But it could barely be thinner stuff.

Or less adeptly executed. Simply put, the movie’s a soggy, sorry mess—with director Brett Ratner apparently deciding that it wasn’t even worth the effort to try to salvage it. He had a point. The first twenty minutes of the picture are astonishingly awful, with an opening diatribe by the screeching Tucker and Chan mumbling his way through bad dialogue and stumbling his way through an ill-conceived chase scene; and though matters improve marginally afterward, they never achieve the modicum of coherence or amusement that would take the flick even to the level of its mediocre predecessors. (At one moment, for example, a diplomat who’s been an assassination target is inexplicably abandoned by all the police guards assigned to watch over him in the hospital, merely to allow Lee and Carter to face a band of bad-guys alone. Plotting like that is way beyond lazy.)

Eventually Carter and Lee make their way to Paris, where the semblance of plot works itself out. Roman Polanski, of all people, turns up as a greasy French cop who abuses our heroes, and the extravagant finale occurs at—you guessed it—the Eiffel Tower. But despite the presence of Max Von Sydow, definitely slumming—very embarrassingly—as a French (!) diplomat involved with the World Criminal Court, the only modestly humorous moments involve a tax driver (Yvan Attal) who’s initially hostile to Americans but learns to want to be one—for the most appalling of reasons.

There isn’t much need to spend a great deal of time on individual contributions to the train wreck, but suffice it to say that Tucker’s shtick is overall as irritating as his eardrum-assaulting voice, and that Chan’s struggle to act and get the English lines right seems more effortful than his acrobatics. Among the supporting players, it’s best simply to forgive Von Sydow’s misguided presence in view of his many distinguished performances in other films, and to note that Dana Ivey, as a nun who can speak French, maintains her dignity in a single scene so raunchy and tasteless that it would have defeated most actresses. The behind-the-camera crew have better luck than the cast, but for what must have been an expensive production, the picture still has a glassy, over-lit look.

Like a car with a sputtering motor that eventually gives up the ghost, “Rush Hour 3” ends with more of the out-takes that have long been a staple of Jackie Chan movies. In this case even they’re sub-par—a fitting end to a movie that, in a summer that’s seen a series of terrible sequels with “3” in the title, is the worst of the lot.