I went to replace the ceiling exhaust fan in our laundry room and noticed the dead fan and the area around it was warm and moist. When I took the fan out I felt the dryer exhaust coming through. The dryer was running. Is that normal for a ceiling exhaust fan to be connected in any way with the dryer?
Jason, no it is not normal to have an exhaust fan of any sort connected to the dryer vent line. The reason is because of what you found when replacing your laundry room fan: moisture in the ceiling and surrounding area. And where there is moisture, mold and mildew can soon follow.
Most exhaust fans remove moisture and odors, but none remove as much moisture as those that service dryers dealing with wet clothing. In addition, dryer vents also accumulate lint and other debris that, if not cleaned on a regular basis, can become a fire hazard.
If the dryer vent is connected to another exhaust line, that lint may find its way into the other line and miss being removed. When it builds up enough, the exhaust fan is no longer working properly, there is a potential for mildew, and it may possibly become a safety issue. For this reason, it is against the Building Code to have an exhaust vent to a dryer vent in many localities. If your home has had the two lines connected since it was new, there's a good chance it's something that was missed by the building inspector.
My suggestion would be to separate the two lines as soon as possible. When you do so, be careful that the dryer vent meets manufacturer guidelines regarding the maximum line length. If you don't know the maximum length permitted for your particular dryer, check on the manufacturer's website under your model number. When you're figuring length, make sure to add in the additional footage for any elbows that may be in the run. Exceeding the maximum length may result in lint buildup in the line which could cause a fire. There should also be a maximum length listed for the exhaust fan, but it isn't quite as critical because it normally only affects performance and efficiency.