It is unclear what you are asking.
Are you asking about the person giving consent or the person receiving consent?
Are we referring to a person that is consider incapable of providing consent?
If you can provide more details about the scenario, it may be more clear.
Alcohol will cause a person to be intoxicated and unable to give consent long before they are unconscious or unable to speak or to feel or see things. If the person is sufficiently intoxicated that they do not fully understand the situation and what it is that they are agreeing to, then that is not consent.
For a layperson that has no experience in assessing intoxicated individuals, there is no hard and fast rule to guide whether the person is intoxicated and unable to give consent. Saying that they were not unconscious and were able to perceive their environment, though, is not an indication that they are able to give consent.However, a rule that I told my son when he went off to college was that if they are too intoxicated to drive, then they you should assume that they are too intoxicated to give consent for sexual activity.
Actually, it is more likely that she was simply intoxicated, as many people do not remember the period of intoxication and may assume that they were asleep. Some people can sleep when leaning against structures that are able to provide sufficient support, but it is more likely that a person that is asleep would not remain upright leaning against a sink.
However, whether she was asleep or so intoxicated that she cannot remember the incident, she would not be considered able to give consent in either case.
Sadly, having sex with an unconscious female happens more than most people realize. Just earlier this year, there have been two widely publicized cases (at Stanford and Florida) involving people breaking up such incidents, and there are likely many others that never get broken up and/or never get significant media attention.
It would be difficult to assess level of intoxication after the fact. Many police officers have some experience in being able to assess intoxication level, so the testimony of the police officers that arrived 10 minutes later may be more valuable than the testimony of other laypersons in the room. While a relatively new police officer may not yet have much experience either, the best that may be able to be done in this situation would be for his attorney to question the police officers about their assessment of her level of intoxication.