Is a witness statement saying that I said committed a crime enough to convict?

Certainly with the facts you've given, it is impossible to tell if this is enough.  The District Attorney would probably have more evidence than a witness statement if they are planning to bring this to trial.  Also when the witness is cross examined, their statement may not stand up at trial.  You need to discuss this case with a criminal defense attorney as soon as possible and present to them all the facts in your possession.  

If this is an eye witness, it is pretty damning evidence. Proof of guilt has to be beyond a reasonable doubt. If there is doubt, there won't be a conviction.  You need to discuss strategy with your legal counsel.  If you did the crime, there is eye witness testimony and you know this is a serious crime, trying to see if a plea bargain is available to you.