I don't know if it's legal, but it's dangerous. I knew someone who tied the leash of his two big dogs to his handlebars to exercise them. Worked well until they spied a squirrel. He wound up with a broken collarbone.
He recovered from that only to have even worse luck.
He decided jogging with them early in the morning, before the Sun rose, was a better idea. They were working on the bridge on the road he chose to jog down, so the only way across the bridge was to run down the traffic lane. He figured that was a little dangerous in the dark, so he figured he'd just run down and across the creek instead. It being dark, he didn't notice that the bridge had an abuttment that dropped about twenty feet straight down instead of a nice gentle slope. One of the dogs broke his fall, but he still broke a couple vertabrae in his back. The dog died. The other dog ran for help. A passing car ran over the dog and killed it. The driver was able to hear the injured jogger's calls for help when he stopped to try and help the dog.