Is there a formal statement or opinion in the Catholic Church regarding martial arts? I have two kids. We don't do contact sports, but some of our friends are involved in American football or hockey, and there's plenty of contact, but it seems like a game. Indeed over the course of my life, such sports have tended towards more game less violence through tweaking their rules. Wrestling seems definitively like a contest not based on violence. Boxing I have no defense for, but it's not part of my question.

I just witnessed my son's friend's dojo, and the weaponry and actions of the participants sickened me. Now it's possible I'm being a pansy, and the CCC allows for self defense, but it sure seemed the participants were leaving communion in their actions.

So, is there a formal statement regarding martial arts within Catholicism? Is there a line in which crossed one has sinned?
On the Vatican website, Google finds one document which specifically references taekwondo.
It's the record of a General Audience given by Pope Benedict XVI on 9 April 2008, and the reference appears only in the Italian version (as it was a greeting directed to Italian speakers, after the main address):

Saluto gli atleti che partecipano ai campionati Europei di Taekwondo, incoraggiandoli a promuovere anche attraverso questa disciplina sportiva il rispetto per il prossimo e la lealtà.
I greet the athletes participating in the European Taekwondo Championships, encouraging them to promote the sport through the respect for others and loyalty.
Original in Italian

The Catechism  of the Catholic Church has two entries for &quot;Violence: force&quot; in its index, and none for &quot;self-defence&quot; or &quot;martial arts&quot;:

1735 Imputability and responsibility for an action can be diminished or even nullified by ignorance, inadvertence, duress, fear, habit, inordinate attachments, and other psychological or social factors.
2306 Those who renounce violence and bloodshed and, in order to safeguard human rights, make use of those means of defense available to the weakest, bear witness to evangelical charity, provided they do so without harming the rights and obligations of other men and societies. They bear legitimate witness to the gravity of the physical and moral risks of recourse to violence, with all its destruction and death.103
103 Gaudium et Spes 78 § 5

Earlier paragraphs (ibid.) do mention anger and hatred:

2302 By recalling the commandment, &quot;You shall not kill,&quot;93 our Lord asked for peace of heart and denounced murderous anger and hatred as immoral.
Anger is a desire for revenge. &quot;To desire vengeance in order to do evil to someone who should be punished is illicit,&quot; but it is praiseworthy to impose restitution &quot;to correct vices and maintain justice.&quot;94 If anger reaches the point of a deliberate desire to kill or seriously wound a neighbour, it is gravely against charity; it is a mortal sin. the Lord says, &quot;Everyone who is angry with his brother shall be liable to judgement.&quot;95
2303 Deliberate hatred is contrary to charity. Hatred of the neighbour is a sin when one deliberately wishes him evil. Hatred of the neighbour is a grave sin when one deliberately desires him grave harm. &quot;But I say to you, Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven.&quot;96
93 Matthew 5:21
94 Summa Theologica II-II 158 1 ad 3
95 Matthew 5:22
96 Matthew 5:44-45

Thus, [to answer the question about a line crossed] to the extent that martial arts do not involve anger or hatred, they are not contrary to the moral law. Practising and training in them involves skill, and it is training for self-defence; dojos are also places of absolute authority and detailed rules, mirroring what might be expected in life. Pope Benedict expressed this in his remarks about respect and loyalty.