If the name is logon.src you need to do a virus scan, and try Spybot.
if the name is logon.scr then this file is totally legal, it's a windows screen saver. you can close it.

if it is "logon.src" like you said it is a virus.
but if it is "logon.scr" it is the screen saver process, mostly it is save, because it is windows default process if you enable screen saver...

Hey I have a problem with too logon.scr
when I start the computer in normal mode instead of loading the user nothing happens, but when I give safe mode, so it appears to me after about 15 minutes and write it logon.scr. I will be OK and off it: ((before, only black screen with the mouse pointer, as in normal mode)
sorry for the mistakes I Czech x)