No radiation is involved in ultrasound imaging. Ultrasound is a method of viewing the inside of the body through the use of high-frequency sound waves. It is a useful way of examining many of the body’s internal organs, including the gallbladder, kidneys, spleen, pancreas, liver, bladder, and the heart.
Yes, there is significant radiation. Every object in the universe emits electromagnetic radiation. The greatest radiators in this situation would be the people and the lights in the room. The ultrasound equipment would probably emit radiation comparable any other electronic device (e.g. a computer). None of this radiation is dangerous, as it is "non-ionizing".
You are probably confused with X-ray machines, which employ low-intensity (but still significant) "ionizing" radiation in the form of x-ray light.