I don't have a basement but know people who shoot suppressed .22 in their basements all the time. They simply don't make it a habit of telling anyone in code enforcement about it.

My grandparents owned a rather large home above the Rose Bowl in Pasadena, CA (it's now the HQ of the Moonies oddly enough). There was a bowling alley in the basement and at five years old I was allowed to shoot my grandfathers 1911 in the far lane any time I wanted. Sadly, hearing protection was not used back then...