I need a non denominational or Catholic church within walking distance of your hotel. Thank you!1
St. Dominic's Catholic Church is very close, at 630 E St. SW. Their web site can be found by googling their name. Note - only walked by - never actually attended.
I don't know of one, but call the hotel concierge and they can tell you for sure!
Get an answer from Residence Inn Washington, DC/Capitol staff and past guests.