We are now in a position to consider how to do radiocarbon dating on an alien planet. First of all the planet would need a good amount of nitrogen in its atmosphere to produce a measurable quantities of C-14. We can measure both of these and if someone hasn't been setting off atmospheric nuclear explosions we can assume that the amount of C-14 is close to the equilibrium value. Since the C-14 is in equilibrium we can't measure the C-14 removal rate, λ, but we could conceivably calculate the neutron capture cross section based the neutron flux in cosmic radiation in order to get the rate constant for the production of C-14, α. The formula relating α and the equilibrium value of C-14, Beq, can then be used to determine the relaxation time, λ. So we would have all that we need to know how to do everything from scratch. Just doing radiocarbon dating would require the C-14 equilibrium value and the C-14 decay rate, β.
Mars is not a likely candidate planet since there is not much nitrogen in its atmosphere (2.7%). Saturn's moon Titan would be a better choice (98.4%). The presence of carbon sinks on a planet might indicate the existence of life but there are purely physical sinks like acid rain that need to be considered.