Rama (the Mapa) 695:4 says (all translations are my own, and you shouldn't rely on their accuracy):
And a woman is obligated in matanos laevyonim (gifts to paupers) and mishloach manos (the sending of foods) like a man, and a woman should send to a woman and a man to a man but not vice versa so that he not come to send to a widow and they come under a safek kidushin (inclarity about whether there is kidushin (marriage)), but by matanos laevyonim one need not worry.
Mishna B'rura comments:
"And a woman is obligated", etc.: [...] And Magen Avraham wrote:
I haven't seen people careful about this; perhaps it's only for a widow, whereas the husband of a married woman sends on her behalf to a number of men. In any event, one should be stringent.
(Examination of the MA shows that his headword is "And a woman is obligated". Also that he wrote "a number of people" where MB quoted him as having written "a number of men".)
P'ri M'gadim explains the MA:
... and when she's married, the authority (r'shus) of her husband is upon her; and a widow and virgin are obligated.
Make of all that what you will, and, of course, CYLOR for a practical ruling.