!!! SPOILER WARNING !!!
This description contains Spoilers for Dangan Ronpa 1!
Talk to Kyouko? (I can roleplay as the character Kyouko, so if you're interesting in having a conversation with her just say so.)
Kirigiri is a cold, stoic woman who never has a lot to say, however when she does, you best listen and hang on to every single word she speaks. Throughout any situation she is someone who is able to stay calm, as someone who will analyse, and investigate her surroundings, rather than talk to the other students. She never reveals much about her past, due to the amnesia she suffers; which is made-known within the game, once her memory returns; and Kirgiri is the first student to notice that Monobear had done something to their bodies, knowing he was the one who had planted said amnesia inside her own body. She is someone who finds it difficult to trust others, especially because of her past as all of her life she has needed to fend for herself; never allowing herself to rely on any other person, but herself. To say she is emotionless would not be a stretch, if something does bother the teen; as stated, she simply doesn't show it, which gives off the aura about her that she is cold, and mysterious, which is due to her no-tolerance attitude.
She is very intelligent, quick witted and blunt, someone who also manages to catch onto things easily, and can also be harsh, depending on the situation. Although Kyouko means no harm by it; her past is the reasoning behind her turning so cold, but she prefers to search for clues on her own, without the help of the other students. At times, if not at all, she is the only student to find out crucial details, leading to the cases being solved, and often has to push Naegi to accuse the culprit, helping him with the clues in the crime scenes. Often enough during the trials, she is able to let the true culprit slip-up with her words, and her own accusations which frames them in the end.
Kyouko is somebody who never says anything that is not necessary, and has stated this before that she is very consistent and she hates small talk, only deeming it very unnecessary. One thing we learn about her early on is that someone has been lost for her, and she has a very estranged relationship with her father. She despises and detests his nature and him, however one reason for her agreeing, and coming into attendance at Hope's Peak Academy was because her father is the headmaster of the school, and she wanted to speak with him one last time, to tell him she was cutting all ties. Kyouko states that she suffered from amnesia, which is why she could not remember anything before arriving at the school, even her own Super High-School Level title, but she realises later in the game that Monobear had done something to her body and she becomes frustrated and angry, demanding to know what he did to her. She detests it when someone asks her many questions, especially of her past and this reverts Kyouko back into her frustrated state - where she becomes frustrated with said person, as she much prefers to be and act alone.
Therefore, when you have done something that bothers her, you will know, and she will ignore you until you make it up to her, or if she manages to get over it. During one instance, she can been seen as hypocritical, when some of the students ask her questions about her past, or her SHSL title; she refuses, but when those students she is questioning, down right refuse to answer her own questions; Kyouko becomes annoyed that they are keeping their secrets to themselves. Within time she comes to trust Naegi, confiding in him about her past, and her own concerns within Hope's Peak Academy. Within her Ice Queen image, it causes many of the students to distrust Kyouko, as she is not able to remember her past, or her title; the students become wary of her, as it would come across as suspicious to the rest of the students.
She much prefers to wander off on her own, without the other students due to her detective title and skills, and if there is a clue to finding out the mysteries - you best believe she will figure them out. Her own attitude is calm and collected, but the mention of her father turns her into a mess, as she has only spoken of him to Naegi, although during the course of her time within Hope's Peak Academy; her wish to meet with her father, and have words with him is her goal, to letting go of her past and moving on with her life. Kyouko still believes all this time her father ran away because he hated his family, and that he became Hope Peak Academy's Headmaster so he wouldn't be seen as a failure of a man. This causes Kyouko to fall into a dilemma, during Chapter Six she and Naegi both enter her fathers secret office, on coming here the door is locked with a password- which Naegi realises is her first name, Kyouko. From thinking her father doesn't give a damn about her, Kyouko's attitude changes for a moment where she realised, maybe he did care and thought about her. This is further put into place after the bones of her father are found within a box inside the office, and the childhood photo of Jin Kirigiri and Kyouko sat on a dresser. However coming to terms with her father's death, after wanting closure of their history and wanting to know why he left her as a child becomes a lot for Kyouko to handle, and she asks asks Naegi to leave, to give her some space and time to come to terms with her father's death; which shows that obviously she cared for him as well, even if she never stated it.
Her main role within Dangan Ronpa is primarily acting as secondary support to Naegi, helping with the clues and within the crime scenes and giving guidance to the evidence presented out in the crime scenes, and due to her detective title, she guides Naegi to help finding out the truth-- even if she has to push him herself.