We have a Leak in laundry room coming from the baseboard. On the other side of the wall is the Garage where the leak is also coming from the baseboard. The Water Meter is inside the house in the laundry room where the leak is coming from. What could the root cause be to this leak?

Let's first determine if this is a drainage or a pressure leak. Look at the water meter.
Is the little pointer moving when all the faucets are closed? Is the leak worse when the washer's discharging? Let me know, Tom

We first noticed the leak and it started after the washer got off balance and was running. As long as the water is on, the leak flows. We haven't turned the washer back on since the leak.

To add to Tom's, since it is no a drain leaking, has to be a Hot or Cold water leak. Determine hot or cold.
If Turning off the Washer doesn't stop the leak,
Why not use the washer, or is it sitting in water?
A plumber or yourself will likely have to open the wall.

We first noticed the leak and it started after the washer got off balance and was running. As long as the water is on, the leak flows. We haven't turned the washer back on since the leak.
Are you saying that, with the washer off and the supplies still open you have water comingt out of the base board until you turn the supplies off? You haven't given me enough details for me to answer. What's turned off? The washer? The supplies? Or both?: Did the water start leaking when the washer pump discharged. Do you still have a leak after the supplies are turned off? Please furnish me with all the information that you can. Cheers, Tom

Yes the washer is now off but we turned the main on this morning to take showers and noticed it coming from the baseboards again when the main is shut off it quits, the washer I do not think is a factor anymore at this point, and I agree I think I may have to open the wall, I can tell the previous owners have had work done here cause there is new drywall in the garage in the spot where the leak comes from, I am thinking maybe they used pvc pipe in there?? And it somehow broke busted or came loose??

I agree that you have a pressure leak. The washer dancing around with a lopsided load must have broke a supply in the wall. Open the wall up, turn the water on for a few seconds and check it out. Let me know what you find. Tom