If you put forward a hypothesis: these molecules were produced by life, then other scientists will search for arguments to disprove your hypothesis. If after some time none of those arguments hold up to scrutiny, we must assume the hypothesis is correct.
If NASA finds something indisputable like an RNA fragment, basically every scientific mind on the planet will try to find explanations that don't involve life. If all abiotic arguments are disproven, then by elimination we've proven that the molecule was produced biologically. If even one argument can conclusively prove an abiotic process that can produce exactly what we observe, then we must assume the no-life case. This is where we are now.
Once the scientific community reaches consensus, the call is made implicitly when the hypothesis is accepted as fact into the scientific canon. The announcement will likely go through various global leaders and/or NASA, as it's an announcement that impacts our entire species, not just one country.
Note that proof by elimination is only one method of proving a hypothesis. Most of the others don't apply here.