It is possible for an object to exhibit characteristics of both comets and asteroids. These objects are known as "main belt comets" or "asteroid-like comets. They are objects that spend most of their time in the asteroid belt but display comet-like activity, such as the emission of gas and dust, when they approach the Sun.
C/2013 A1 (Siding Spring) is an example of a main belt comet. It was observed in 2013 and displayed a bright coma (the glowing envelope around the nucleus) and a short tail. Despite its cometary activity, C/2013 A1 (Siding Spring) orbits in the asteroid belt, and it is believed to be a dormant comet that was reactivated by a close encounter with Jupiter.
So, while it's not common for a comet to feel like an asteroid, it is possible for certain objects to exhibit characteristics of both types of celestial bodies.