The normal way to check professional background is by calling back references included in an applicants resume. You can do it by yourself or contract a Human Resources outsourcing company to do it for you.
If your applicant's resume does not include a References section, request it.
When checking background with former employers, check first with HR department, then with former inmediate supervisor.
If you hire professionals, you can set as a requirement to have an exequatur (if it applies) and to be associated to the applicable Colegio Profesional. (CODIA for engineers, architects and "agrimensores", Colegio de Abogados for lawyers and Colegio Medico for MDs).
You can report a professional to the applicable Colegio if he/she scams you or his/her professional performance represents a serious risk to society. If that is the case, they will expulse him/her from the Colegio and/or ask their exequatur to be removed.
As usual, if the employee is well connected, most probably he/she will not be punished at all.
You can try a lawsuit and apply the Labor Code to separate him/her from your company.
Welcome to the Dominican Republic.
Jess