We have the Platinum Edition of CRD on my desktop PC. Can I keep that and download a copy on my laptop?

I am wanting to run the reports on the laptop and still work from my machine.

I think going by the functionality listed here:

http://www.christiansteven.com/EditionFunctionality.htm

you would need to have the Enterprise Edition or above to have multiple installations. Good thing is at the least you stand to gain the other functionality as well such as custom action types, insert functions etc

Cheers