* Close (to shut) vs. Close (near)
* Content (satisfied) vs. Content (the material inside something)
* Conduct (behavior) vs. Conduct (to lead or guide)
* Current (happening now) vs. Current (a flow of water or electricity)
* Desert (a dry, barren area) vs. Desert (to abandon)
* Digest (to break down food) vs. Digest (a summary)
* Entrance (a way in) vs. Entrance (the act of entering)
* Minute (very small) vs. Minute (a unit of time)
* Object (a thing) vs. Object (to oppose)
* Present (a gift) vs. Present (being in a place)
* Produce (to make) vs. Produce (fruits and vegetables)
* Record (a written account) vs. Record (to set a new best)
* Refuse (to decline) vs. Refuse (trash)
* Seize (to grab) vs. Seize (a type of fish)
* Tear (to rip) vs. Tear (a drop of water from the eye)
* Wind (to turn) vs. Wind (moving air)
There are many more homographs out there, but these are some common ones that start with the letter "c."