Yes you can download it again the same way if it is the same version Windows or Mac. Which one did you download to the chromebook? What is your laptop?
How to download your purchase
https://ttlc.intuit.com/community/installing/help/how-do-i-download-the-software-i-purchased-at-turbotax-com/00/26075
Access your downloads here
https://shop.turbotax.intuit.com/commerce/account/secure/login.jsp?pagecontext=download