Other candidates seeking the congressional seat so far are Democratic state legislators Ben Diamond and Michele Raynor, former Obama administration official Eric Lynn and Christian Hotchkiss.
Olszewski testified Tuesday that she secretly recorded a phone call in June she initiated with Braddock in which he claimed the purported Russian-Ukrainian hit squad would respond quickly if he made a single phone call.
A civil trial begins before a Florida judge in a stalking case in which Luna, a Republican congressional candidate, is accusing a former rival of harassment and claiming he could hire a Russian and Ukrainian hit squad to have her killed.
A friend of Luna's, Erin Olszewski, also sought a permanent restraining order against Braddock.
Crist previously was Florida governor as a Republican and has held or run for several other elected posts.
No criminal charges have been brought.