Before it hits the road, every car first lives digitally on an automaker’s computers, where engineers can keep track of engines, electrical systems and every other detail.

Chrysler, the struggling U.S. automaker that owns the Dodge and Jeep brands, has quietly taken a step away from engineering software market leader Dassault Systemes and signed an important piece of its design business over to rival Siemens, according to sources familiar with the dealings. On its own, the deal is just one big customer making a switch. But Siemens and some other Dassault rivals are hoping it’s the beginning of a larger shakeup in the auto engineering software market.

Dassault declined to comment on the Chrysler account in detail. “Chrysler has not announced any decision to move away from DS solutions,” a Dassault spokesman told Fortune. “Chrysler continues to heavily use DS design and manufacturing solutions to execute their five-year plan announced on November 4, 2009.”

Some in the auto industry have played down the significance of Chrysler’s move to Siemens, pointing out that Fiat, Chrysler’s new managing partner, already uses Siemens and may have pressured its new vassal to do the same. (Siemens insists that Chrysler made the decision on its own.) But Dassault may have a bigger problem on its hands: Chrysler isn’t the only automaker considering a change.

Rivals pounce

Siemens says several Dassault customers have expressed interest in its engineering software, NX. “They know that they have a problem,” says Eric Sterling, executive vice president of global marketing for Siemens PLM. PTC, another rival, also sees an opening, says Jim Heppelmann, the company’s chief operating officer. He said PTC has recently won several large customers from Dassault, including Volvo and ArvinMeritor.

At issue is the structure of computer-aided design software for cars. Automakers use CAD programs to digitally model and test auto parts and manufacturing. Product lifecycle management software, or PLM for short, pulls together all of a car’s engineering data. IDC estimates that the worldwide PLM market for automotive, aerospace and defense is about $3.3 billion, with auto accounting for about a fifth. Dassault is the biggest player with about 22% market share; Siemens and PTC have 13% and 12%.

The latest version of Dassault’s PLM offering, CATIA V6, is built in a way that critics say locks customers into using other Dassault products to manage data. Think of it as an auto industry spin on iTunes: Just as songs from Apple’s iTunes Store would initially play only on iPods, Dassault’s engineering software is made to work exclusively with Dassault’s data management system.

That’s potentially a major problem for customers like BMW. Peter Spies, director of geometric development for the carmaker, says he is happy with Dassault’s CATIA V5 software. But upgrading to V6 would mean ripping out some of BMW’s tailor-made data management systems and replacing them with more Dassault offerings — a move he can’t stomach.

“Without any benefit to our business, we can’t pay more for all their software — it must be an open solution,” Spies says. Ideally, Dassault would back off of its proprietary stance and let V6 work with other programs. In the meantime, BMW is testing Siemens NX.

Open vs. Closed

The open vs. closed debate is reminiscent of a trend that’s popular in Silicon Valley these days: rather than just sell individual products, lots of folks seem to want to sell their technology in a package. Apple (AAPL) has a closed approach with its iPhone and iPad, which are tightly bundled with Apple’s proprietary operating systems and app store. Oracle (ORCL) bought Sun in part so that it could create servers that are specially tuned to run its databases. And Cisco (CSCO) is selling specialized servers and other equipment that has its networking software baked in.

When the closed strategy works, it can yield outsize profits — Apple’s recent financial results being a prime example. But it can backfire, too. If a company’s bundle of products doesn’t work together well enough to justify the added cost, customers can get turned off.

That’s the danger for Dassault. Joe Barkai, analyst at IDC Manufacturing Insights, says that in this age of consolidation, automakers are more likely to be looking for flexible design systems that can easily share data with a new partner or supplier.

If automakers follow Chrysler’s lead and balk at the closed approach, Dassault may have no choice but to retool its software to play nicer with other vendors.