Im sorry about your brother's condition.
Yes there is a connection, mental disorders can also affect one's personal maintennance or hygiene that's why in some cases, some develop conditions that are related to it. for example, oral hygiene is neglected, the result is plaque, gingivitis and tooth decay which leads to halitosis.

But in some cases of bi-polar, hormonal changes occur and the salivary flow is also affected by the emotions so the less salivary flow, the more acidic the saliva becomes which makes the bacteria stick to the tooth a lot more and it will also lead to halitosis.