The Dominican Republic’s Internal Revenue Office is called the Dirección General de Impuestos Internos (DGII). Whether you have Dominican residency (cédula) or not, you are required to declare your income after spending 182 days in the country. You should only pay tax after your 3rd taxable year as a resident. KPMG have published an up-to-date tax guide in English which details all the information foreigners will need.
Insurance for expats
The Dominican Republic has a reliable and developed private medical care infrastructure and it is strongly advised that expats take out private health insurance. Though the country has a state healthcare system it is far from adequate - especially if you are used to western variants like the British NHS. See the health section of this guide for further information.
Home insurance is also strongly recommended - even if you are only renting. See the housing and rentals guide for more information.