How do I find out if my deceased parent filed their 2015 tax return?

Unfortunately, a death in the family is made only more burdensome and disquieting by the taxation system.

Until the "scammers" took over this past year, the IRS offered an online service to provide transcripts and account records directly online.  Now the process is more cumbersome and the transcripts and account records are postal mailed.  See links below.  The process will take anywhere from 2 to 4 weeks as the IRS is, apparently, understaffed.

If you mother was employed, check with the past employer for a copy of a W-2.
If she had bank accounts or brokerage or mutual fund accounts, check for Form 1099-INTerest, 1099-DIVidend  and 1099-Brokerage.  Also look for monthly or quarterly statements, or email notifications of same if she used email.

Check to see if there is either a check or direct debit in her bank account with the payee being either the U.S. Treasury or the state of residence.  Alternatively, in the next several weeks, watch for a direct deposit of a refund, or receipt of a check.

Here are the several relevant IRS web pages:

• https://www.irs.gov/Individuals/Tax-Return-Transcript-Types-and-Ways-to-Order-Them
• https://www.irs.gov/Individuals/Get-Transcript  by mail
• https://www.irs.gov/uac/Newsroom/How-to-Get-a-Transcript-or-Copy-of-a-Prior-Year-Tax-Return

When you have this first matter resolved, come back to get instructions on the complex multiple tax filings that may be necessary - for income and deductions prior to death on Form 1040 and for income and deductions subsequent to death on Form 1041.