By bodily fluids, I am assuming you are talking about a blood draw? If so, then in a VERY general sense, they do have the right to take a blood draw. However, the best route for the police to take would be to obtain a search warrant.
The United States Supreme Court has recently addressed this issue. Some states have a law that says you MUST submit to blood testing if asked if an accident with injuries has occurred (this is the case in Illinois). Without an accident, the police may take blood, but there must be enough probable cause that you were DUI in order to get a Court to issue a warrant.
Nonetheless, there are exceptions to the warrant requirement. One exception is called Exigency, which essentially means an emergency or situations where time is of the essence. The Supreme Court has said, however, that the fact that alcohol may dissipate gradually over time does not establish an exigent circumstance.
So, to answer your question, with a warrant, the police can take blood from an individual, provided all the steps and procedures are met by the police.