Many people think that if you are at CMMI L2, you don’t have to have process description. They believe process description is required only in L3.

Absolutely, this is not right. If you look at the Reference Book, at GP2.2 text title “Establish and maintain the plan for performing the process”, think a little and remember CMMI is a model not a process, it does not describe exact activities to be done, so don’t depend on it as a process. The point is how could you plan the project without knowing the activities done in planning. However the model doesn’t leave us to conclude, it states in “Generic Goals and Generic Practices” chapter the following:

“The plan for performing the process typically includes the following:
• Process description
• Standards and requirements for the work products and services of the process
• Specific objectives for the performance of the process (e.g., quality, time scale, cycle time, and resource usage)”

It even states to have measures for the process, stated in the plan:
“Measurement requirements to provide insight into the performance of the process, its work products, and its services”

So prepare a process description and include the level of detail that is suitable for the project, and each project could have his own process description that is suitable to the project type and size. At level 2 you don’t have to have organization wide process repository and a
tailoring guidelines, this is required in level 3 and above.