What did you file with a due date of 3/31 ?  

Your return's electronic filing status history records all e-filing activity related to the return, including the Electronic Postmark. You can print it out if needed. 

TurboTax Online

https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp  -- enter the Social Security number of the first taxpayer on the return and the ZIP code to retrieve your filing status history.

TurboTax CD/Download software

(Windows) From the TurboTax File menu, select Electronic Filing > Show Electronic Filing Status History.
(Mac) From the TurboTax File menu, select Check E-Filing Status.

E filed but no refund yet

@harryrowlands

https://turbotax.intuit.com/tax-tools/efile-status-lookup/

TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.

Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 20 of your Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

On the IRS site you are also offered the use of an app called IRS2Go

https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others

If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.

https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-pr...