You can try Fourier Transformed Infra-Red Spectroscopy for the same. Solid dye sample can be pelleted by using KBr and liquid dye sample can be run on liquid analysing assembly of this instrument.
For accuracy, if you can identify the dye, you can see the empirical formula and get the accuracy of that dye structure. Otherwise, you will get an initial idea about the dye and can further characterize it by using other sophisticated instruments (Chromatograms).
Rest I would suggest to wait for more expert to sort out your query.
First you must sure that sample is composed from one component.
Then you can use FTIR spectroscopy. The resulting spectrum you must search in spectral library, or try to read with the help of IR functional groups tables. Also you can use the help of an IR specialist.