The lawyer of the woman at the centre of the case, Ines Madrigal, told reporters outside the court they would appeal against the decision. The statute of limitations imposes deadlines on courts to complete legal proceedings.
Madrigal, who was told by her mother at 18 that she was adopted, accused Vela of forging her 1969 birth certificate to show her adoptive mother, now dead, as her biological parent.
Vela, who had denied the charges, was the first person prosecuted over the "stolen babies" scandal that affected thousands during general Francisco Franco's rule.
Many of the cases date back to the right-wing dictatorship of 1939-75 when campaigners say officials took babies from "unsuitable" mothers - often communist or leftists - and gave them to families with connections to the regime.
A decade ago, a Spanish judge recorded the cases of about 30,000 Spanish children taken at birth during Franco's rule.