It may not be an ask situation, but it might be a requirement to avoid paying exit fees.
For example, it is necessary that a DR resident to produce a valid residency card or potentially pay an exit fee for an overstay upon leaving.
Likewise if a person was naturalized and has Dominican Citizenship, they could present their Dominican Cedula which is the version citizens get which does not have No Vota on the back and is indeed the proof you asked about regarding DR citizenship. It is all that most Dominicans have to prove citizenship.
That cedula would prove their citizenship upon leaving along with whatever passport they were using so they don't need to pay a potential exit fee for an overstay. No law requires Dominican Citizens to have and travel on a Dominican Passport that I am aware of.
A DR resident is a different case and the cedula may apply.
I would accept that in order to clarify citizenship and avoid exit fees Dominicans with any other nationality and traveling with an overseas passport may show their cedulas instead, however; two rebuttals to that theory:
- The proper document for traveling and immigration purposes is a passport
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A passport does shows the citizenship and place of birth (hence cedula isn't necessarily needed as the passport already has this info)
- I have yet to see anyone using a cedula at the airport as mean of traveling documentation, much less for immigration purposes
- I don't believe a cedula along would be accept it at immigration, regardless of original nationality