Residency
This is taken directly from the Dominican Republic US Embassy wedsite:
Residence Visa
The residence visa is the first step to obtain the residence card in the Dominican Republic. This visa can be obtained in approximately three months. The Ministry of Foreign Relations recommends that the process begin prior to the person arriving in the DR, although it can also be carried out once the person is in the country. In order to apply for a residence visa you must submit the following documents:
Letter of application signed by the applicant or legal representative and addressed to the Consul or, in case the person is already in the DR, the Minister of Foreign Relations
The letter of request can be issued by an individual or a company .
If the application is filled out by an individual it should contain: individual's name, nationality, place of residence, and the activity to which the applicant is or will be dedicated in the country.
If the application is filled out by a company, in addition to the data on the applicant, the request should be made on company stationary, and signed by the highest ranking officer of the company, indicating the position the applicant will hold.
Indication of the ties to the country, that can be any of the following:
1- Dominican nationality by origin.
2- Marriage to a Dominican.
3- Work contract, legalized by the Ministry of Labor.
4- Proof of economic solvency (investors, retirees).
Form 509-Ref, duly completed and signed by the applicant, to be submitted with the other documents to the Consulate or Ministry of Foreign Relations if the person is already in the Dominican Republic.
Certificate of Good Conduct issued in the jurisdiction of origin. If the beneficiary has been more than three months in the Dominican Republic, it needs to be issued by the competent local judicial authority.
Medical Health Certificate. Issued in the jurisdiction of origin. If the applicant has been living more than three months in the Dominican Republic, a recent medical certificate should be presented, legalized by the Ministry of Public Health (SESPAS).
Three front view 2"x2" photographs.
Birth Certificate.
Certificate of the Department of Migration with proof of the last entry of the person to the country and copy of the Tourist Card.
Two photocopies of the applicant's complete passport.
Observations:
All documents received from abroad need to be legalized by the Dominican consulate in the corresponding jurisdiction.
All documents need to be presented in original and four copies with the exception of the passport.
The passport needs to be valid for a minimum of three months after having been deposited for the visa.
If the application includes the spouse, a marriage certificate should be included.
Minors are exempt from the Good Conduct Certificate requirement
Clearly since they encourage you to apply through the consulate you do not have to be in the Dominican Republic to begin the process.