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There has always been a great deal of debate about Ophelia's death in Shakespeare's Hamlet. My sense is that there is nothing in the play to prove for certain if there was intent on Ophelia's part to kill herself. Gertrude's speech seems to note that Ophelia's death was an accident, as the Queen describes the event in Act IV, scene vii:
There on the pendant boughs her crownet weeds
Clambering to hang, an envious sliver broke,
When down her weedy trophies and herself
Fell in the weeping brook. (187-190)
In essence, Gertrude personifies the branch that was holding Ophelia—it was "envious" (translated also as "jealous"), therefore inferring that it was not her choice to go into the water, but that she was taken in by the breaking of the "sliver."
Gertrude goes on to note:
Her clothes spread wide
And, mermaid-like, awhile they bore her up;
Which time she chaunted snatches of old lauds,
As one incapable of her own distress,
Or like a creature native and indued
Unto that element... (190-195)
The Queen is noting that after the branch broke (and we can infer because of her insanity), that Ophelia is seemingly unaware of the danger she is in—because she keeps singing—or that she felt as one with the water, like a creature at home in its "native" element.
Gertrude's description allows the reader to believe that the death was an accident brought about by her madness, for had she been sane we can assume that she would never have climbed out onto the branch because she would have been aware of the danger there.
The reaction of the gravediggers, called "Clowns," in Act Five, scene one, signifies a belief that Ophelia took her own life. One gravedigger states that if a man goes into the water and drowns himself, it is suicide. But if the water comes to a man, the man "shortens not his own life" (19). The coroner, the First Clown notes, has ruled it an accident. The Second Clown notes that only Ophelia's elevated social standing allowed her a Christian burial:
Will you ha' the truth on't? If this had not been
a gentlewoman, she should have been buried out o'
Christian burial. (22-24)
If we refer to Gertrude's description again, it would seem that the water did, in fact, come to Ophelia, but the gravediggers seem to infer that suicide took place, and some critics and scholars agree. Personally, I believe Ophelia was unaware of what she was doing.
Gertrude is giving all the details of what happened before Ophelia's death. How she put flowers in her hair, went to the river where she got into the water. Her clothes firstly were holding her up, but then dragged her down. She was certainly in distress and most likely suicidal, though in her state of mind she may not have known what she was doing. The symbol that points to actual suicide is Gertrude saying "mermaid-like", since in most northern cultures mermaids were maidens who committed suicide by drowning.