Crude oil by itself is a combination of a multitude of hydrocarbon fuels. Hydrocarbons can already be changed from one to another with clever (but often expensive) chemistry. So, I am going to assume that we can generalize the question to:
Can human raw remains be turned into fuel based hydrocarbons?
The answer is yes, if you really wanted to.
The decomposition of human bodies would normally follow other decay mechanisms. Of most interest for your purpose is Methanogenesis; and from such, methane.
Methane is a simple hydrocarbon fuel, and, on its own, is not generally strong enough for the most intensive of activities. But for basic purposes, it should suffice; where it doesn't, one can spend energy and change it to a more appropriate compound (where this energy will be obtained is beyond the scope of this answer.)
There is another issue, the one of volume and efficiency. In a sense, how much methane can one get from this method. To answer this, we look to wetlands.
Wetland methane emissions is the primary natural methane source. The Global Carbon Project estimates that between 2000-2012 era, wetland methane emissions totaled about 167 teragrams, Tg, (184.1 short tons, or more curiously, by Wolfram|Alpha, ~40% of the mass of all alive humans) per year. This is a lot of methane.
However, the world's annual oil production in 2010 was 31.82 billion barrels (5059 Tg). (Wolfram|Alpha)
Therefore, your world may easily have human corpse based natural methane production. However, in order for it to be physically viable, it must be on an industrial scale. I suspect it must also be the cultural norm; else, I suspect opposition to it will make it nonviable (not enough human corpses). This is something to keep in mind. Moreover, as previously noted, methane is not perfect, and its usage may be limited to simple operations (not too far from before standard combustion engine era), but I do not claim to have much idea about this.
Finally, there are a lot of logistics and issues with large based methane producing grave sites. Depending on one's energy needs and era, human incinerators may actually prove to be effective after a large amount of methane is gathered. They can be used as power plants, or provide energy to turn CO2 to CH4 through Methanogenesis, or turn methane into more complex petroleum products (akin to your crude oil in the first place).
In one way or another, human crude oil plants aren't a good way to get energy, just to recycle it.
TL:DR Yes you can; it will take a rethinking of culture and it must be a large scale undertaking to accomplish, but it can be done. It will be expensive, complex, and really (current day) unethical. But, for oil...anything.
