Yasiel Puig -- State DROPS Case Against MLB Star ... Our Bad.

Seems the cop in the Yasiel Puig case overreacted when he said the Dodgers star could've killed his mom on a FL highway ... because officials have now dropped the reckless driving charge saying Puig is nothing more than a common speeder, TMZ Sports has learned.

We posted the video of the crazy arrest ... in which Puig, sporting pink shorts, was pulled out of his Mercedes and berated by an angry Highway Patrol Officer who caught the MLB star doing 110mph with his mom in the car.

At the time of the Dec. 28th arrest, the cop insisted Puig was driving recklessly and hauled him to jail. If convicted, Puig could have been sentenced to 90 days in jail.

But today the State dropped the case against the 23-year-old ... saying speeding alone on an open highway doesn't constitute "reckless driving" and he wasn't doing anything else to warrant a charge other than "speeding."

So in the end ... Puig gets a speeding ticket ... and that's it.