A common thing I've heard growing up is that women living in Israel in the 1st century couldn't be witnesses in a court of law because [reasons].
The times that I've heard this said it has also normally been preceded by something along the lines of "...the first Christian evangelists in the world were women because Jesus appeared to Mary and Martha first and instructed them to inform the other disciples, who were men. This is amazing because..."
In Jewish Law, women are not valid witnesses, as it states in the Mishnah (Shevuot 4:1):
שְׁבוּעַת הָעֵדוּת נוֹהֶגֶת בַּאֲנָשִׁים וְלֹא בְנָשִׁים
The oath of testimony is conducted with men and not women
The Talmud expounds on this and says (Shevuot 30a):
מנהני מילי דת"ר (דברים יט, יז) ועמדו שני האנשים בעדים הכתוב מדבר
How do we know? Because our Rabbis taught: "Two men shall stand." (Deuteronomy 19:17)
So during First Century Israel, where these laws were practiced by the Jewish community, it would be logical to say that women would not be valid witnesses. (Even today this is Jewish Law.)
If you have any other questions concerning Jewish religious practice or law, feel free to ask at Mi Yodeya, the Judaism Stack Exchange of which I am an active user.
In the 1st century, Judea was a Roman province. There were actually a wide range of systems in use in Judea in the first century AD, but the Graeco-Roman system was the one available to everyone in the province.
Roman law was quite explicit in permitting women to swear oaths and testify in court.
The Digest of Justinian states:
The fact that the Lex Julia [legislation introduced by Augustus in 23 BC] on adultery forbids a woman found guilty to give evidence shows that women have the right to give evidence at a trial.
A number of other references to women being able to appear in court as witnesses appear in Book 12 of the Digest of Justinian.
[Although the Digest of Justinian is a compilation that was put together much later (in the 6th century), the laws were often enacted much earlier - as in the case of the Lex Julia mentioned above].
Furthermore, in his trial against Verres in 70 BC, Cicero called several women as witnesses. In his speech, he shamed Verres for having forced him to compel respectable women to appear in court to testify against him. Cicero's objection here is clearly against disturbing women of station, and not against trusting their testimony, otherwise why would he have called them as witnesses?
Indeed, we have a number of examples from ancient Egypt (another Roman province, but one where we generally have more surviving epigraphic evidence from the period) of women being allowed to testify in court:
One example (P.Oxy. 1.37) dated to 49 AD, which was copied from an official government archive, shows that a woman's testimony was entered into the court record.
Another example (BGU 4.1105), from a case in Alexandria in 10 BC, records the testimony of a woman who testified in court against her husband for divorce on a charge of wife-beating and squandering her dowry.
(The translations appear in Greek, but Google Translate should be able to make a decent fist of translating them into English. I'll try to locate English versions & update the answer later, when I'm not typing on a phone screen.)
While Jewish law may have maintained that women could not serve as witnesses in certain criminal and civil cases there was an exception for instances in which only one witness was required. Women could testify in matters concerning someone's death, so they could probably testify to a resurrection should that ever be required by a judge in court. Usually, a judge had discretion over whom he would allow to give testimony anyway.
Yevamot 87b reads:
"And we also learned in a mishna (122a): They established that they would allow a woman to marry if her husband was reported dead by one witness, based solely on what he learned from the mouth of another witness, i.e., hearsay testimony, and also the testimony of a woman who heard from another woman, and even the testimony of a woman who heard from a slave or from a maidservant. Apparently, one witness is deemed credible in this regard, as whenever hearsay testimony is accepted, the testimony of one witness is also valid"
