What is Gertrude's answer? Does this suggest anything about the queen's role in the death of her first husband?Act 3. Scene 2 Hamlet asks Gertrude...

Player Queen 

Nor earth to me give food, nor heaven light! 
Sport and repose lock from me day and night! 
To desperation turn my trust and hope! 
An anchor's cheer in prison be my scope! 
Each opposite that blanks the face of joy 
Meet what I would have well and it destroy! 
Both here and hence pursue me lasting strife, 
If, once a widow, ever I be wife! 

HAMLET 

If she should break it now! 

Player King 

'Tis deeply sworn. Sweet, leave me here awhile; 
My spirits grow dull, and fain I would beguile 
The tedious day with sleep. 

Sleeps 

Player Queen 

Sleep rock thy brain, 
And never come mischance between us twain! 

Exit 

HAMLET 

Madam, how like you this play? 

QUEEN GERTRUDE 

The lady protests too much, methinks. 

HAMLET 

O, but she'll keep her word.

Gertrude says that the Player Queen "protests too much." About what? The Player Queen says, in effect, that if her husband should ever die, she would never remarry... under the penalty of "lasting strife" or continuous inner conflict.

Now, Gertrude's answer may imply some uneasiness about the death of her first husband, Hamlet's father, and her hasty re-marriage, but it hardly shows her complicity in his murder.

It is not until after the play-within-a-play, when Hamlet confronts Gertrude in her room (Act 3, scene 4), that Hamlet gets his mother to even consider the possibility that Claudius murdered his father, King Hamlet. Indeed, the ghost of Hamlet's father implies that the Queen is innocent when he says to Hamlet (Act 1, scene 5):

But, howsoever thou pursuest this act, 
Taint not thy mind, nor let thy soul contrive 
Against thy mother aught: leave her to heaven 
And to those thorns that in her bosom lodge, 
To prick and sting her.

Leave her alone, he says. She is innocent of the murder and will go to heaven, but she will suffer there for being so naive and shallow.