How the hell could it "help with a murder investigation" to provide them with a sample of your DNA?
Presuming you are innocent, you are simply opening yourself up to a false positive match, either now or in sometime in the future.
You have everything to lose, and nothing whatsoever to gain.
In the case of a degraded DNA sample, it's possible to have the statical odds of you being a match for a sample in the range of 100,000 to 1. That doesn't seem so bad unless you consider that there might be 1,000,000 records on file. Statistically that's 10 database hits, and if you are the lucky one cold hit, combined with the apparent belief that juries find scientific evidence infallible, you could easily be convicted. It *has* happened before that the only evidence that links a suspect to a crime is a cold database hit.
Just don't give them a sample without a court order, ever.