Cracking Down on Double-Voting?

KXNT News Las Vegas, a CBS affiliate, reports today that a woman has been arrested for attempting to vote twice.  The woman, a registered Republican, is accused of voting at a polling place in Henderson and then attempting to vote at another polling place in Las Vegas on the same day.  Officials say that this indicates two things: "...we take all elections complaints very seriously and investigate them thoroughly[,]" and "... this demonstrates the integrity of the system."

Good job to the authorities.  However, there is another aspect that is not mentioned in the report.  Identity theft is a major problem in the country today.  How do authorities know that the vote in Henderson was not cast by an identity thief?  According to a report from January 2012, also from CBS News Las Vegas:

Right now Nevada voters do not always have to show identification.  When you go to vote, a poll worker will ask you to provide your address or date of birth, and you sign the voter roll.  If the signature matches, you're allowed to vote.  If it does not match, the poll worker is supposed to ask for identification.

So they may have checked ID if the poll worker felt that signature did not match, but was there such a request?  Can the original signature be retrieved?  If this is the case, would it not require an expert analysis to determine authenticity?  Wouldn't it be easier to just require positive ID in the first place?