I have two W-2 forms both from companies in California. I am filling out my taxes using Credit Karma's new tax website. It will only allow me to enter a single set of values from one of the W-2's, not both. Assuming that that's correct, I'm guessing I'm supposed to use the values from the W-2 of the company I currently work for (starting in June 2016), rather than the W-2 from the company I was working for earlier in 2016. Is that all correct?
When entering multiple W-2s on you tax return, the totals from all the W-2s will be used in the other worksheets. If you insist on entering only one, then you should follow quid's advice from the comments and enter the sum from each box.
The bigger problem here is that the IRS uses the totals from your W-2s to match the (electronic) copies of the W-2s that they received from your employer. At the very least it will flag your return for errors and cause more scrutiny. I would suggest that you use another provider for filing your taxes.