Isolate the nucleic acid, then try to digest it with DNase or RNase. That should tell you which backbone. Then certain RNases at least are specific to ssRNA or dsRNA.
Like Lehman has suggested, you may need to first extract the genomic content of your sample before detecting if it is made up of DNA or RNA. You may then run Southern and Northern blotting protocol to detect the type of genetic material. Also, with good number of aliquots from the extract, you may run different assays on each of the aliquots. Like digesting with RNase and then running a PCR protocol using beta-2- macroglobulin primer or digest with DNase and then run PCR protocol using beta actin primer.