According to Preach My Gospel, the official LDS (Mormon) missionary guide, missionaries are supposed to ask potential converts
Have you ever committed a serious crime? If so, are you now on probation or parole? Have you ever participated in an abortion? a homosexual relationship?
The book later explains:
Question 4 in the baptismal interview asks if a person has been involved in a serious sin, such as an abortion, a homosexual relationship, or a serious crime. What should I do if someone confesses such a sin?
...Do not schedule a baptismal date or make any promises about whether they will be cleared for baptism and confirmation. Express your love and review the principle of repentance. Kindly explain that these sins are serious and that a person with more maturity and experience (your mission president or someone he assigns) will talk with them and help them with these matters. Then send a baptismal interview request directly to the mission president.
From context, the items other than crimes that are listed in the same passages are all related to reproductive or sexual issues, so one could infer from context that "serious crime" only refers to sexual offenses or crimes against children, but I'm not sure that that is how it is actually supposed to be interpreted.
According to LDS teaching or practice, what crimes are "serious" enough to require escalation of a baptismal interview to the mission president? I'm guessing that neither jaywalking nor second degree mopery with intent to deface a postage stamp would count as "serious", but how serious would a crime need to be before this clause would apply? Gambling violations? Using a product in a manner inconsistent with its labeling? Possession of a firearm without a license, but without intent to harm anyone? DUI first offense? DUI second offense? DUI fiftieth offense? Operating a Ponzi scheme? Voluntary manslaughter? Murder only? Is this based on a holistic judgment call made by the missionary, or are there strict interpretive guidelines defined somewhere? For example:
- Only felonies "count", misdemeanors are not serious enough to warrant escalation to the mission president.
- Only crimes that would "shock the conscience" of an average Mormon count. If an average Mormon would react to the revelation of a crime in a convert's past with "whatever, meh, yeah I did that a few times too", then it doesn't count and the baptism can proceed without the involvement of the mission president.
- Only crimes that would "shock the conscience" of an average local citizen (whether Mormon or not) count.
- Only crimes that create a victim count, "victimless" crimes like possession of drugs or unlawful weapons don't count.
- Only crimes that would constitute a per se violation of the Ten Commandments count (borrowed from a possibly somewhat similar if you squint concept in Roman Catholicism).
- The LDS church has a schedule of "harm thresholds" for various statutory offenses above which an offender's participation counts as "serious", for example committing tax evasion in an amount over $10,000, possessing more than 100 grams of cocaine, defacing more than 10 postage stamps in a 48 hour period, or possessing more than 2 unregistered machine guns, counts as serious enough to require the mission president to become involved.