I have read that in northern hemispheres, most female songbirds can't sing (for example, the Blackbird). Things are different in tropical regions. Birdsong is for males in some species; it is utilized to defend territories and/or attract other females.
While it seems impossible that female songbirds can't perform complex songs, can it be possible for captive birds?
I have read some reports that females are able to sing after being injected with testosterone. But the interesting question is whether females can be trained to sing without testosterone injections or other interventions?
There is an article showing that for one songbird species it is possible to produce female birdsong without testosterone injection (while older research claimed, females sang only when treated with this hormone): https://www.newscientist.com/article/2151727-female-birds-that-used-to-be-silent-are-now-singing-like-males/
There are dissertations about birdsong and sexual hormones: https://research.vu.nl/ws/portalfiles/portal/42186406/complete+dissertation.pdf
And here it is reported that female songbirds sang after getting testosterone: https://journals.sagepub.com/doi/abs/10.3181/00379727-41-10631?journalCode=ebma