Hi there,
I had this same question, below is part of a reply I received from the owner of the Romany DNA Project on FamilyDNA.
Basically he is saying through the autosomal test (which gives you a broad continent %age of you dna) you may or may not see a small south asian %age and this test really is inconclusive.
I had my autsomal test done through ancestry.com. I will next be putting the results through FamilytreeDNA
https://www.familytreedna.com/products.aspx.
This site matches your dna with other peoples, so you use your dna to build your family tree and this way can build a picture if there is a romany lineage.
I believe that you can do a deeper dna test which is the "Fathers line" or "The mothers line" on the Family dna site. However for this to work, the romany ancester has to be your fathers fathers father (and so on etc etc) or mothers mothers mother (etc etc).
In my case the potential romany ancester is my fathers mother, so I can't use these tests.
Good luck! Here is his message:
" ... You may or may not show a small South Asian percentage on your autosomal report, but that hasn't as much meaning to me, what does have more meaning to me is matching existing Romany participants and there are multiple Romany whom have done the autosomal test. I do not put a lot of faith in to the admixture population reports because those reports are grossly lop sided towards the European population, so it may find some percentages to certain populations like the Romany, or may not find any at all.
I know of male Romany "Rom" whom are in Y Haplogroup H1a - M82 which is clearly South Asian in origin, but their autosomal reports shows zero percent South Asian. Because of admixture, the mixing of Romany and Europeans over the last 1000 to 2000 years, Romany on an autosomal genetic level are more European today then South Asian. What has more meaning to me personally is the DNA matches you will have because that is really what that test is more about, finding related family members whom share autosomal DNA with you. The autosomal test works exactly as it was intended, I found two cousins through that test, one is my paternal grand mothers nephew, and one is my grand aunt's grand son, so the test is best if used for it's primary purpose, to find related family members and not 100% rely on what the admixture report has to say because those admixture reports are heavily biased towards the European population.