how do the laws affect rape investigations?

Answer 1

The laws define all elements of a crime, whether it be rape, murder or theft. The laws also define the defenses to each crime. The investigation focuses on collecting enough evidence to prove each element of the crime, beyond a reasonable doubt, or determining if a defense exists and can be proven.

Answer 2

I'm not sure I understand your actual question. There are "rape shield" laws that prevent criminal defendants from making an issue of the past sexual conduct of the rape victim, but that doesn't have to do with the investigation necessarily.