The authority board may determine that the whole or any part of an obligation of the authority assessed or contracted for pursuant to Act No. 185 of the Public Acts of 1957, being section 123.731 to 123.786 of the Michigan Compiled Laws, or the drain code of 1956, Act No. 40 of the Public Acts of 1956, being section 280.1 to 280.630 of the Michigan Compiled Laws, shall be defrayed by special assessments against the property specially benefited. The special assessments may be levied and collected in accordance with this act except as provided in this section. The requirements of section 18 with respect to a petition and section 19 with respect to a hearing do not apply to any special assessments levied and collected pursuant to this section and Act No. 185 of the Public Acts of 1957 or Act No. 40 of the Public Acts of 1956.