Shameless Self-promotion - Toronto Star's DIY Garage

Ah, TPMS. This was actually a false warning, proof that even a $120,000 BMW isn't flawless...

You can find my Toronto Star DIY Garage article on correctly setting Tire Pressures here.

It is amazing just how many people don't understand that the correct pressure to set your tires at is not on the sidewall, but on the car. This goes for technicians, too. Most got into the trade years before TPMS (Tire Pressure Monitoring Systems) became common, and the techs that they apprenticed under almost certainly were never taught this. I know I wasn't.

To be fair, standardized tire pressure labels didn't appear until the mid-2000's (when US law required them to be located in the driver's door jamb area). Before that point, if your car even had such a label, it could have been hidden damned near anywhere - glovebox, fuel filler door, front door or jamb, rear door jamb, inside the trunk lid, inside the centre console lid... you get the idea.

In reality, the same size and load index of tire might fit several dozen very different vehicles, and the sidewall only lists the maximum working pressure for that tire, which is what determines that tire's maximum load capacity. Automakers regularly use different pressures front and rear to adjust handling and wear characteristics, even using the same size tires at both ends. Setting the pressure to the sidewall max can result in a 44psi tire on a 26 psi car; it'll get awesome fuel mileage from the lower rolling resistance, but at the cost of greatly reduced grip, far harder ride quality, and substantial wear to the centre section of the tread.
(Trivia factoid: stunt drivers often crank the pressures up to make their cars slide around more easily.)

TPMS makes setting pressures accurately more important, but it's worth noting that not all TPMS systems will flag overinflation.

Find your label, get a decent quality tire gauge (I like digital myself), and check your tires occasionally. They'll last longer, you'll be safer, and you may even save a little bit of fuel in the process.