The Dominican Republic has two police forces – the Policía Nacional (national police) and Cuerpo Especializado de Seguridad Turística (tourist police, commonly referred to by its abbreviation, Cestur).
Cestur officers are generally friendly men and women whose job is specifically to help tourists. Many speak a little bit of a language other than Spanish. They wear white shirts with blue insignia and can usually be found near major tourist sights and centers. You should contact Cestur first in the event of theft, assault or if you are the victim of a scam, but you can equally ask them for directions to sights, which bus to take etc.
It’s best to have as little interaction with the Policía Nacional as possible. If a police officer stops you, be polite and cooperate; heavily armed roadway checkpoints aren't uncommon, particularly in regions bordering Haiti – they're looking for drugs and weapons. They may ask to see your passport – you’re not required to have it on you, but it’s a good idea to carry a photocopy. You might also be asked for a 'tip' in cash or merchandise; feign misunderstanding or simply politely decline. More often than not, you'll simply be waved through.