Can we just use some documents we created for our customer's process to be ML2?

In a recently completed contract, our company provided support which included helping a Federal agency implement process improvements and achieve a CMMI level 2 maturity rating in CMMI for Acquisition. Personnel from our company developed, documented, and implemented the processes with input, approval, and oversight from the government staff.

Our management asked whether there was any way to use the documentation developed in that contract as evidence in a level 2 appraisal for our company’s CMMI-SVC efforts.

Is there any way that process documentation (methods and evidence) can be used in a CMMI-SVC Level 2 appraisal of our company’s processes?

Of course they did! :)

You have probably heard the SEI joke that the answer to everything is “it depends!”

A CMMI SCAMPI Appraisal is an evaluation of your business practices, behaviors, processes, and deliverables. To the extent that what you developed for your client has been embraced and adopted by YOUR company, and you can demonstrate that is “the what things are done around here” then there is no issue with you re-using process documentation created for another client.

But if your thought is that you will just present this documentation to a Lead Appraiser, without adopting it for your own use, then I doubt that would be useful for you. If it did make it possible for you to achieve CMMI-SVC ML2 under these conditions, then I would question your Lead Appraiser’s competency (or ethics)!

That all said, the SVC and ACQ constellations may share 16 Process Areas, but the target stakeholders of the practices are much different. The way they are adopted is much different. So, adoption of the processes you developed for your client with ASQ may not be a good fit for your 

business.

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Is there a simple book with a set of steps for achieving CMMI ML2?

We are a small business that provides federal government contractors and  staffing augmentation to various state and local government agencies. We are finding that more of the federal work we are going after requires at least CMM Level 2.  I am trying to understand the easiest way that we can get to the level 2 benchmark. Can we simply document our backoffice processes. Do we need to also document our CRM & HRM process? Where do we start? I think our situation is much simplier than documenting a full SDLC methodology. Is there a simply book that says follow these steps? Please advise.
The CMMI for Services, which sounds like the "flavor" (or constellation) of CMMI that you would use, has 25 Process Areas.  In Maturity Level Two there are eight process areas that must be satisfied and appraiser using an external SCAMPI Lead Appraiser.
Those eight process areas are: Project Planning, Project Monitoring and Control, Measurement and Analysis, Configuration Management, Process and Product Quality Assurance, Supplier Agreement Management, Requirements Management, and Service Delivery.
In order to achieve Maturity Level Two you must demonstrate sustained, consistent processes performance in all the Process Areas, with the POSSIBLE exception of Supplier Agreement Management.  You demonstrate this by defining, using, and then being appraised on your company's standard processes.
You probably have less work to do in the CRM/HR area than in the area that focuses on the development, maintenance, delivery, and monitoring of your company's services.
These processes don't come out of a book - they are YOUR processes, so it would be difficult to write a book that was specific to your company.
Your best bet is to get smart about the CMMI by taking the CMMI Intro class from an SEI Partner, download the CMMI-SVC specification from www.sei.cmu.edu/CMMI (only read Part 2 for now!), and then engage a professional to help you navigate the roadmap.