The issue is that the paper ballots are counted electronically. There may be a paper version for double-checking the vote, but it's rarely used. The vote relies almost entirely on electronic technology.
There are many state-mandated post-election audits that involve random selection of ballots or precincts. There are state statutes and procedures that require a post-election audit of ballots after every election. These audits are designed to verify that voting equipment and tabulations operated correctly and that reported totals are accurate