We don't know of any hard-and-fast rule about who can void a check. However, our practitioner expert Judy Bicking calls attention to who should NOT void a check; this relates to segregation of duties.
For those who are able to segregate duties, the individual voiding a check should not be anyone involved in vendor maintenance or invoice processing to eliminate the potential for fraud.
For some small and midsize companies, segregation of duties is impossible, so as a compensating control, they either require a second signature or have this work assigned as part of a regular audit.
Some companies allow the person who creates the check run (or else someone in accounting) to call the bank to notify them of the void. The invoice processor or customer service rep usually performs the research. That way, there are two sets of eyes to ensure there is legitimate backup supporting the void. Note that supporting documentation is required for the escheat process.