I live in Michigan. The temperature has been below zero at night. Last night when I got home from work hot water was coming from the spout in the master bath tub without the faucet being turned on. I turned the hot water off at the water heater. The cold is fine. Also the water is not draining from the tub. I tried a bottle of liquid plumber in the gel form and plunging but neither did the trick.

Sounds like frozen Pipe can you chase any pipes down and check for freeze? Is the vent clear for thei tub? Really sounds like a frozen trap in tube and bat water lines frozen can you get any heat there or blow heat toward tub/waterlines. Is there a service panel to open to expose tub and shower water lines if so heat low and catch tub water trap that froze.
Hope this helped Signed 21 boat

The hot water running with the valve off is a just a leaky faucet. Please let us know what make and model faucet you have. May just need to replace a washer or cartridge. If your tub doesn't drain, it could be a frozen drain line, or just coincidence that the facuet started leaking and the drain plugged up at the same time. Most likely if the drain is on an outside wall, this is what happened. Faucet started to leak, causing very little water to run down the drain, water started to freeze in drain and just kept freezing until complete drain was frozen sollid. Find the source of cold air hitting drain, fix cold air problem, then put as much heat directly in the area of frozen drain as possible. Once you get the drain working, fix the leaky faucet. Please let us know what you find. Take care.

Lee

Mygirlsdad77 has good thought.

If the tub drain/trap froze more than likely the cold side to supply faucet froze too. That cold line can get into the faucet and expand the seats and pressure the cartridge and open the hot to run anyhow that's a possibility and so is Mygirlsdad77 but if the faucet was dripping/running hot water that would help stop the trap/drainage from freezing and keep it thawed out.

Just to clarify, you say that you have water at both cold and hot in the tub? Its just the hot is dripping or running? If you have water flow at both hot and cold, then your water lines are not frozen(yet). Please look into drain and let us know what you find.