This is non-commercial use ?
1. My customer is government. They don't get profit with the PC.
2. They will download CTM.
3. I will setup the PC and install CTM. This generate profit for my company.
Since your customer will download the program (CTM), and you are charging a service fee for setting up your customer's PCs including installing programs for them (which includes CTM), I think it's alright as you are not selling a Free program, CTM in this case, to make a profit.
or I'll download it. Does this produce a different result?
If you download it yourself then you will be suspected of selling a Free program and making profit from your act.
Edit : Actually it would be fine for you to download CTM for your client, provided you shall make it clear to them that CTM is a Free program and you have not charged them for the provision of the program.