Wendy Williams at Hospital to Determine Mental Capacity

Wendy Williams is at Lenox Hill Hospital in New York City for an independent examination as to whether her cognitive functions are sufficiently intact to end her guardianship.

Sources with direct knowledge tell TMZ ... a caregiver not associated with the guardianship -- Gina Monterroso -- ordered the trip and the test ... this after the NYPD paid a visit to Wendy Monday morning to determine if, as Wendy says, she's effectively being held prisoner.

The NYPD has asked about Wendy being confined to the memory unit of the assisted living facility, where she cannot leave the floor without permission. She rarely gets out.

In addition to NYPD, Adult Protective Services has launched its own investigation into the guardianship. They interviewed Wendy's niece, Alex Finnie, Monday.

TMZ broke the story ... Wendy would like famed lawyer Joe Tacopina to take on her case. Tacopina is seriously considering it. If this happens and the judge doesn't end the guardianship, there will almost certainly be a jury trial where jurors will determine if Wendy has sufficient cognitive functions to end the guardianship.