Exactly. Around here we have red light cameras. If they catch you speeding or running a red light, they mail the ticket to you with your court date on it, or, if you choose, the amount of the fine, and where it can be paid.
So the old woman refused to sign the ticket. All that means is that she was disagreeing with the citation. Nothing prevented the cop from giving her the ticket anyway, noting that she refused to sign. The court date has been delivered to her that way. If she fails to show up for court, or to pay the fine, then the judge simply issues a bench warrant for "failure to appear" and the pick her up and take her to jail.