Is Tarawih Compulsory for Females?
Question

 
Is Tarawih prayer required for women?
Which is better for women, to perform Tarawih at home or in a mosque?
Praise be to Allah.Is tarawih compulsory for females?
Tarawih prayer is not obligatory for women, and it is still better for them to perform the Night Prayer at home. Prophet Muhammad (peace and blessings of Allah be upon Him) said:
"Do not prevent your women from going to the mosque, even though their houses are better for them." (Reported by Abu Dawud in al-Sunan, Bab ma ja-a fi khuruj al-nisa ila'l-masjid: Bab al-tashdid fi dhalik. See also Sahih al-Jami', no. 7458)
Whenever a woman prays in a place that is more private and more hidden, that is better for her, as the Prophet (peace and blessings of Allah be upon Him) said: "A woman's prayer in her house is better than her prayer in her courtyard , and her prayer in her bedroom is better than her prayer in her house." (Reported by Abu Dawud in al-Sunan, Bab ma ja-a fi khuruj al-nisa ila'l-masjid. See also Sahih al-Jami', no. 3833)
Umm Humayd, the wife of Abu Humayd al-Sa'idi reported that she came to the Prophet (peace and blessings of Allah be upon Him) and said: "O Messenger of Allah, I love to pray with you." He said: "I know that you love to pray with me, but praying in your house is better for you than praying in your courtyard, and praying in your courtyard is better for you than praying in the mosque of your people, and praying in the mosque of your people is better for you than praying in my mosque." So she ordered that a prayer-place be built for her in the furthest and darkest part of her house, and she always prayed there until she died. (Reported by Imam Ahmad; the men of its isnad are trustworthy. )
But the fact that praying at home is preferable does not mean that women are not permitted to go to the mosque, as is clear from the following hadith:
`Abdullah ibn `Umar said: "I heard the Messenger of Allah (peace and blessings of Allah be upon Him) say: 'Do not prevent your women from going to the mosque if they ask your permission.'" Bilal ibn `Abdullah said, "By Allah, we will prevent them." (Ibn `Umar) turned to him and told him off in an unprecedented fashion, saying: "I tell you what the Messenger of Allah (peace and blessings of Allah be upon Him) said, and you say 'By Allah, we will prevent them'!!" (Muslim, 667)
Conditions of women going out to the mosques 
But there are conditions attached to the permission for women to go to the mosque , as follows:

She should wear complete hijab.
She should not go out wearing perfume.
She should have the permission of her husband.

Her going out should not involve any other kind of prohibited acts, such as being alone in a car with a non-mahram driver. If a woman does something wrong like that, her husband or guardian has the right to stop her; in fact it is his duty to do so.

I asked our Shaykh, 'Abd al-'Aziz, about Tarawih prayer in particular, and whether it is better for a woman to perform this prayer in the mosque . He replied in the negative and said that the hadiths that state that it is preferable for a woman to pray in her house apply to all prayers, and this includes Tarawih as well as others. 
For more, please see this category: Tarawih prayers and Laylat al-Qadar
And Allah knows best.