If a petition contains more than 1,000 signatures, the city secretary or other authority responsible for verifying the signatures may use any reasonable statistical sampling method in determining whether the petition contains the required number of valid signatures, except that the sample may not be less than 25 percent of the total number of signatures appearing on the petition or 1,000, whichever is greater. If the signatures on a petition circulated on a statewide basis are to be verified by the secretary of state, the sample prescribed by Section 141.069 applies to the petition rather than the sample prescribed by this section.