Yes you can copy your files (both .tax and .pdf) to your laptop computer. They are usually stored in Documents in a TurboTax folder.
If you used a TurboTax Online account to file a prior year return:
1. Sign-in and load My Tax Timeline (you may have to select this from the drop-down in the upper-left)
2. Load My Tax Timeline is displayed on the lower-right (scroll-down if necessary)
3. Choose the year you wish to access. Once chosen, click Download/Print Return (PDF)
Note: This feature will be locked if any unpaid version of TurboTax was used to file.
If any CD/Download version of TurboTax was used to file, the information prepared is only stored in your personal files. You may request an exact copy of your return from the IRS for a fee. You can also request a tax return transcript at no charge. For either, see here: https://ttlc.intuit.com/questions/1901218-can-i-get-a-copy-of-my-tax-return-from-the-irs