We do know that complex hydrocarbons (e.g., tholins) exist in the outer Solar System. Some geologists maintain that at least some oil on Earth is of non-biological origin. The mainstream, though, tends to discount their views. Is it possible to verify the hypothesis empirically and what should we look for in geodata to have it substantiated or disproven?
One possible key is isotopic fractionation via biological processes - see dating the development of the C4 photosynthetic pathway, and specifically isotopic fractionation between carbon-13 and carbon-14. δ13C from volcanic degassing is markedly different to that from biological sources; the arguments for human involvement in climate change (see e.g. the IPCC) rely on the changes in δ13C since the beginning of the Industrial Revolution: the value has shifted markedly towards that of the hydrocarbons we've been burning from its pre-Industrial value. (As for how we know atmospheric δ13C for CO2 prior to the Industrial Revolution - the answer is polar ice cores!)
Thus the arguments for/against abiogenic oil rest on (1) isotopic ratios, and (2) other geochemical indicator ratios; see e.g. Jenden et al. (1993).
Höök et al. (2010), in a review of the arguments for biogenic and abiogenic formation processes, say:
However, theoretical studies, laboratory verification and discoveries of trace amounts of abiotic oil do not imply the existence of commercially significant deposits. [...] The lack of a clear and irrefutable success in locating abiotic petroleum in commercial quantities is problematic.
This year, Ahmed et al. (2014) advances the argument that Siljan Crater oil is unambiguously of biogenic origin due to the copresence of molecules of "known" organic origin (specifically terpane and sterane biomarkers). As for a definitive answer, [Wang et al. (2014)7 say:
Whether abiotic (inorganic) process can form oil and gas resource is a difficult question that has been explored continuously by scientific community for more than a century but has not yet been solved.