In any misdemeanor case or in any class of misdemeanor cases and in a Class 5 or Class 6 felony case, the chief of police of the city or county or his designee, or the sheriff or deputy sheriff of the county, if the county has no police department, in which the case is pending may notify the accused of the issuance of the warrant or summons and direct the accused to appear at the time and place directed for the purpose of the execution of the summons or warrant. However, the issuing judicial officer may direct the execution of such process prior to any such notification. If the accused does not appear, then the warrant or summons shall be executed and returned as provided by § 19.2-76.