This number seems to come from here:
> The prevalence of suicide attempts among respondents to the National Transgender Discrimination Survey (NTDS), conducted by the National Gay and Lesbian Task Force and National Center for Transgender Equality, is 41 percent, which vastly exceeds the 4.6 percent of the overall U.S. population who report a lifetime suicide attempt, and is also higher than the 10-20 percent of lesbian, gay and bisexual adults who report ever attempting suicide.
Suicide Attempts among Transgender and Gender Non-Conforming Adults
There have been other similar surveys done (which got results varying from 25-43%, as reported in the introduction) but this one is the largest, “with over 6,000 respondents”.