Typically when discussing abortion, many in both the "pro-life" and "pro-choice" camps tend to focus on the infamous Roe v. Wade, 410 US 113 (1973). But Roe was not the first case to address abortion, and it certainly was not the last.
Like many other decisions, the Supreme Court built the jurisprudence of Roe upon the decisions of prior cases. One notable case is Griswold v. Connecticut, 381 US 479 (1963), in which it was decided that the State may not outlaw birth control, but it applied only to married individuals. Building immediately upon that decision is Eisenstadt v. Baird, 405 US 438 (1972), in which the Supreme Court expanded Griswold’s protections to unmarried individuals.
Between these two cases would come another, dealing almost directly with the criminal proscription of abortion.
Dr. Milan Vuitch was arrested in the District of Columbia in 1968 for illegally performing abortions. Judge Gerhard Gesell, however, would set aside the indictment and rule that the statute under which Vuitch had been arrested was "unconstitutionally vague". That decision would be appealed to the United States Supreme Court.
Oral arguments in the case would be held on January 12, 1971, and the case would be decided April 21, 1971. In United States v. Vuitch, 402 US 62, the Court would reinstate the indictment against Vuitch, stating that the law in question was not unconstitutionally vague, but the ruling doesn’t stop there.
Because Vuitch was arrested and indicted under a criminal statute, the Supreme Court ruled that ultimately "the burden is on the prosecution to plead and prove that an abortion was not ‘necessary for the preservation of the mother’s life or health.’" [406 US at 71]
If this burden is not met beyond reasonable doubt, as determined by the fact-finder during the trial, a "not guilty" verdict is compelled. This particular provision is in line with virtually every other criminal statute on the books: the prosecution has the burden of proving beyond reasonable doubt the existence of all facts and elements pertinent to supporting the charges alleged.
Let me repeat that because it is quite important for everyone to remember:
In any criminal trial, it is the burden of the prosecution to prove beyond reasonable doubt all facts and elements necessary to support the charges alleged. In no criminal trial will you find it the burden of the defense to prove the absence of a particular fact or element to secure a "not guilty" verdict.
An element of a crime is presumed absent unless otherwise proven to exist beyond reasonable doubt by the prosecution with cross-examination by the defense.
The central tenant behind the reason the law was originally declared unconstitutionally vague rested on the supposed vagueness of the world "health" with regard to whether an abortion was performed pertinent to the mother’s health. Does that mean physical health only, or does it also include mental health?
Applying Doe v. General Hospital of the District of Columbia, 313 F. Supp. 1170 (DC 1970), the Supreme Court ruled, inline with this decision, that abortions may be performed to resolve or avoid compromising the mental health of the mother, even if she had no prior history of mental health defects. This is the standard that allowed George Tiller to perform seemingly needless late-term abortions.
With the law upheld and the indictment reinstated, Vuitch would face trial on charges of illegally performing abortions. However with the burden now firmly on the shoulders of the prosecution to prove, beyond a reasonable doubt, that the abortion was performed in violation of the statute, prosecutions of allegedly illegal abortions would become difficult.
Vuitch perfectly outlined the difficulty of prosecution with regard to abortions:
Now the government lawyer will be in the position of challenging my medical decision. What are the jury members going to decide when a lawyer tries to tell them that the doctor is wrong about a medical matter? 
Even if abortion were again criminalized today, with the Vuitch standard in place (I don’t yet know of a case where it was vacated), prosecution would still be very difficult.
Other questions, however, were still yet to be answered at the time the Vuitch decision was rendered.
 "Ambivalence on Abortion". Time. May 3, 1971.
United States Supreme Court cases: