When wood rots, it undergoes a process of decomposition that is powered by microorganisms. These microorganisms consume the wood, releasing carbon dioxide (CO2) and other gases as they do so. So, in answer to the question, yes, rotting wood does give off CO2.
The amount of CO2 released by rotting wood will depend on a number of factors, including the type of wood and the conditions under which it is decomposing. For example, hardwoods tend to release more CO2 than softwoods, and dry rot releases more CO2 than wet rot.
The decomposition of wood is an important part of the global carbon cycle, and helps to offset some of the emissions from human activities like burning fossil fuels. So while rotting wood does release greenhouse gases like CO2 into the atmosphere, it also plays a role in helping to mitigate climate change.