The more I watch Tenchi Universe and the more I think about certain scenes and episodes from Tenchi in Tokyo, the more convinced I am that Ryoko and Kiyone have a strong but strange kind of friendship boiling up between them.
When they first meet in Tenchi Universe, Kiyone wants to arrest Ryoko and take her back to Headquarters for interrogation. By the end of the episode, however, it is Ryoko to whom Kiyone is pouring out her woes about Mihoshi, under the influence of some sake, of course! When Kiyone and Mihoshi go to leave the Earth, Kiyone no longer seems keen on taking Ryoko with them to face her charges.
During their trek across space, there are clear indications of an almost surreal partnership between the two. When Yagami is hijacked, it is Ryoko and not Mihoshi who jumps into the cockpit with Kiyone, armed and ready to take on the two errant teenagers. And when they are piloting Yagami across the gravity of the star, it is Ryoko who is in Mihoshi's pilot seat, while Mihoshi is elsewhere. That there should be any kind of friendship between a serious Galaxy Police officer and a wild wanted Space Pirate seems bizarre, but that it exists is beyond dispute.
When Nagi appears on the Earth to challenge Ryoko, having taken Tenchi as her prisoner, Ryoko begs Kiyone to let her settle it herself. Kiyone knows her responsibilities are to intervene, as this is a legitimate case of kidnapping (as she says). But she bows to Ryoko's will and allows the pirate to confront Nagi in her own way. It's interesting, this, since Kiyone is concerned with Nagi's crime and the fact this area is her jurisdiction. And she is keen to send Nagi from the solar system, because bounty hunters are not allowed to operate there. But is this true, or a ruse to keep Nagi away from Ryoko? It's impossible to know, but in all of this legal gibberish she spouts, she makes no reference to Ryoko and the pirate's own crimes. Additionally, when the Jurai ship takes custody of Ayeka, Sasami and Ryoko, Kiyone attempts to have Ryoko released into her custody, as it is her jurisdiction. ^_^.
In Tenchi in Tokyo, it's harder to pick out at the beginning whether or not Ryoko and Kiyone are friends. However, after Ryoko leaves the Earth and is in her hideout with Hotsama, it becomes clear that Ryoko knows the two police officers are undercover within her lair and is allowing them to continue unhindered because their antics amuse her and she's missed their company. More, she even talks to them in the seating area of her ship like old friends, and Kiyone does her best to bring Ryoko round to her way of thinking - trying to help the pirate deal with her ghosts. Kiyone sums up Ryoko's life in a way none of the others have even seen - "Are you happy with your empty life, kicking about aimlessly?".
When the Galaxy Police spring the hideout and Ryoko believes Kiyone and Mihoshi have set her up, she is angry at them and calls them backstabbers - claiming that's why she left the earth, to destroy the world of people who behave like that. It's clear she feels betrayed - and yet, later, when she reflects on it, she realises that she still does miss their company and was amused by their behaviour.
Kiyone is the closest person who comes to reaching Ryoko's core in the Tenchi in Tokyo series - closer even, really, than Tenchi does, because he doesn't understand how desperate or deep Ryoko's feelings for him really run. That Kiyone can show someone who is supposedly her enemy (and whose capture would spark a promotion for her) such compassion proves they do have a bond. And the fact that, even when being complimented and awarded a medal for their good work, Kiyone feels guilty that Ryoko is angry with them also indicates this fact.