Yes, you can (and should) file an extension. Understand that an approved extension is an extention until Oct 15th to ***FILE*** your tax return. It is "not" an extension to pay any taxes that may be due. So if you think you will owe the IRS when you actually do file your return, you need to pay what you think you will owe *BEFORE* the special 2019 extended date of July 15th. You can pay online if you want, at www.irs.gov/payments and remember to print your receipt, as you will need it when you do actually complete and file your tax return.
Finally, if your state taxes personal income you will need to file for an extension with your state too. Then if you think will you owe your state, you will need to pay your state taxes too, separately from your federal taxes. Again, even with the state an approved extension is an extension to *file* and is not an extension to pay.
[Edited 03/26/20 to reflect IRS and state extended due dates]
