In type I Bipolar disorder, people often experience full-blown mania. In Bipolar II disorder, they will experience a milder form of hypomania. In the milder forms (which can also occur in type I), the hypomania may make them feel very good, hypersexual, impulsive. One might almost think of it as returning to being an adolescent, feeling full of energy, somewhat invulnerable. This is certainly something I witnessed in my girlfriend. When she was hypomanic, she would buy things she really could not afford, want to make love all the time, take on new projects. To be honest, it was kind of exciting. I had no idea what was going on, I just assumed that it was her natural personality and it would last forever.
In full blown mania, bipolar people can often completely lose any realistic perspective of the consequences of their actions. Instead of buying a bunch of new shoes, they might take all of their savings and investments and gamble it in a game of roulette. They might feel so invulnerable and confident that they do something incredibly physically dangerous.
In the milder versions, this might lead to infidelity. In the worst versions, they might leave a twenty year marriage because they feel really good, really confident, and they just cannot realistically conceive of the negative consequences of their actions.
In the worst cases, they may require hospitalization. They may hear voices or believe that they are on a mission from God, or they have a cure for cancer, or something they have no realistic chance of ever achieving.
There are basically two halves of the illness that can have serious consequences on personal relationships. One results from feeling really good ([hypo]mania). The other results from depression If a bipolar person is jumping into new relationships, it is probably not because they are depressed. If the decision is based on something absurd, or something that really does not fit their normal personality, then it probably is (hypo)mania.
If he is withdrawing from you, shutting himself off, not talking, I would suspect the depressive phase of the illness. If he is immediately taking up with new girls, it might be the (hypo)manic phase. It is also possible he left during a time of depression, then met someone new when he was stable or (hypo)manic.
If he is threatening to call the police on you for no good reason, you can almost guarantee that is a result of mental illness, probably full blown mania (because that action seems very detached from reality), but only a proper evaluation by a psychiatrist will be revelatory. Bipolar disorders are not the only mental illness that can cause the sort of behavior you describe, but unless he has shared his precise diagnosis with you, you can only guess. Full blown mania is usually a symptom of Bipolar I disorder, which tends to have more negative consequences than the other forms of the bipolar spectrum, because of the possibility for extreme detachment from reality and extreme behavior.
The only way to be sure what you are dealing with is a proper diagnosis. If he is not willing to share it with you or be reevaluated, I think that you should not believe anything he says. If he is an honest person, he probably means everything he tells you when he is stable, but his chances of remaining stable without proper treatment are very low.