Answer
Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
As for your question, there is no evidence in the Qur’an preventing women from laughing in public. Muslims, women and men alike, should only follow the Islamic ethics and teachings concerning chastity and decency and avoid in their talks and laughs any temptation.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
I don’t know where this absurd question comes from. If men are allowed to laugh in public why shouldn’t women? Who are we to legislate for women? Legislation in Islam is the exclusive right of Allah and His messenger. There is no text in the Qur’an putting such a restriction on women.
Therefore, this is at best an example of misogyny and Islam is innocent of it. It is clear from the Qur’an that women are free to speak and express themselves even as men do; they are not to use sexually enticing mannerisms or expressions even as men are not allowed to do.
For more, see these fatwas:
Does Islam Accept Women’s Curses?
Are Women Permitted to Serve on Mosque Boards?
Scope of Men’s Guardianship over Women
Allah Almighty knows best.