More information about what you are trying to do would be helpful.  What dye are you referring to?  What process are you asking about?

Thanks, Rick Manner. I am using Methylene blue dye and in the presence of catalytic compound and UV light, degradation of dye has been observed. Absorption spectra of degraded dye at the different time has been collected, which gives me C/C0 which I have mentioned in the main question. Now what I have is C/C0 vs time and absorption spectra of the degrading dye vs time. Can I calculate the H2 evolution rate from these pieces of information? I use a flask on a stirrer in which dye and catalyst are stirred. there is no any attachment to measure H2 and O2 evolution rate.

I know very little  about the degradation of  Methylene blue dye othe than the molecukr formula (C16H18ClN3S)  if you actually know the decomposition mechanism or at least the decomposition products.   You can speculate about the decomposition mechanism (or better yet find research that identifies the actually decomposition mechanism) to estimate the relative amount of C vs H in the decomposition products. and based on the mechanism predict the ratio of H to C in the decomposition products and the amount of H that decomposes to H2.  I have never studied the decomposition of Dye so I should not speculate about the decomposition products vs time and the mechanism. Do you have any additional information about the decomposition mechanism?

Is photocatalytic degradation of MB produces H2 and O2 gases?

In general ,gas chromatography-mass spectrometry (GC-MS)) is a suitable technique to  investigate the composition of gaseous mixtures.Sometimes,indirect H2 detection depends on stable co-products .I agree with Rick ,the degradation mechanism is useful in your research. 

Clearly something other than pure degradation of the methylene blue is occurring, you would not get H2 and O2 from simple degradation since it contains no oxygen. I think first of all you need to be sure the MB is in fact degrading and you are not just shifting the pH which would also cause a change in the absorption. As mentioned above, you absolutely have to understand the reaction to calculate gas evolution. Can you analyze the content of your solution chemically at all? If you could analyze it at a few points in time and correlate the composition to the absorbance data you might be able to back out the hydrogen and oxygen evolution by deducing what reaction must have taken place to get those results and how much H2 and O2 must have been produced. It is hard to see how you can do this with any confidence if you do not know what reactions are truly occurring.