(

a) The ordinance may also provide that a license to engage in the business of massage may be denied upon a showing by the licensing authority of either of the following:

(1) Proof that the massage personnel and the owners or operators of a massage business have been convicted of a violation of

Section 266i, 315, 316, 318, or subdivision (

b) of

Section of the Penal Code, or proof that the massage personnel or the owners or operators of a massage business have been convicted in any other state of any offense which, if committed or attempted in this state, would have been punishable as one or more of the above-mentioned offenses of this subdivision.

(2) Proof that the massage personnel and the owners or operators of a massage business have been convicted of any felony offense involving the sale of a controlled substance specified in

Section 11054, 11055, 11056, 11057, or of the Health and Safety Code or proof that the massage personnel or the owners or operators of the massage business have been convicted in any other state of any offense which, if committed or attempted in this state, would have been punishable as one or more of the above-mentioned offenses of this subdivision. (

b) The ordinance shall also provide that a license to engage in the business of massage shall be denied upon a showing by the licensing authority of proof that the massage personnel or the owners or operators of a massage business are required to register under the provisions of

Section of the Penal Code.