The laws of physics decree that all manner of processes take place at rates dependent on the mass of the species involved. When carbonates are precipitated from a solution of atmospheric carbon dioxide dissolved in water, the minerals are slightly enriched in the isotope carbon-12 (processes involving the lighter isotope go faster).
Organic carbon compounds formed by living organisms from the same initial atmospheric carbon dioxide are however much more enriched in carbon-12 because biological processing is much more complicated than a simple precipitation. There is therefore a big difference in the carbon isotopic composition of organic matter and carbonate deposited in an aqueous environment subsequently consolidated into a sedimentary rock.
The signature is retained long after any organisms have died, indeed the existence of such fractionation has been the key to showing life on Earth started 4 billion years ago by demonstrating isotopic fractionation in the oldest known sediments.
Manfred Schidlowski, a German scientist has compiled data for some 10,000 different samples and the difference between the isotope ratios in organic and mineral phases show how biosynthesis leaves a ubiquitous signature of life even in specimens where there are no fossils visible.