She is accused of obtaining employment there between July and October last year by deception through making "representations of educational qualifications not held".
A further charge alleges Joseph made a false academic transcript with intent to gain employment.
Both this and the sexual connection charge carry maximum penalties of 10 years' jail, while the other two have seven-year maximum jail terms.
Waipareira Trust's chief executive John Tamihere said it would be inappropriate to talk about the allegations while the matter was before the courts, but said: "We've been fully compliant with the police investigation."
The trust was established in West Auckland in 1984 and provides access to health, education, justice and social services.