Brno generally is a safe city. Anyways, never leave your bag and possessions unattended. A certain (numerous) part of local people have this strange habit to take or rob whatever they see. Well, not all of them. But why to take the risk. When walking the busy streets or standing in a crowd or travelling by a public transport, always hold your bag on your chest, do not hold it loose on your shoulder or back. Do not wear your wallet in your pants' back pocket.
Be carful, when meeting gypsies !
The problem seems to be bigger here in Brno / Brünn than in many other places in Czechia, as the border to Austria is quite near and plenty of day-tourists might make perfect vicitims.
I was "attacked" by several small children between 4 and 10 years, fooling around and trying to get my attention, surrounding me, singing and screaming, and there were some elder gypsies in a small distance...
...and I could escape simply as a heavy rain started.
All of this happened in the large park next to the lovely theatre at around 8.00p.m.
This guy (see picture) is the one you should avoid! Is he a robber? No. Is he a reapist? No. Does he belong to organized crime or mafia? No. Then why should you be afraid of him? Let me tell you. He stole 10 KCz from me. A tief then? No. So what??? Well, as I was walking down the square he aproached to me and asked if I need something. As I told him I was looking for some cyber cafee he offeree me help at once. Look at this map, he said and showed me some hand drawn map. He marked me some internet cafees and give me the 'map'. I thanked him but wait! You own me 10KCz. For this map? LOL! However 10KCz is not a big money, just about one quarter US$, but for that map... Let me tell you at last. Internet cafees he pointed out were some 10-15 min away and later I found one on the same square we stood. LOL
I was renting a room in a typical private residence about one mile from the center of town. One afternoon, after getting off the tram and walking a short distance to the building's front door, I started unlocking it and suddenly felt a slight pressure on my rear pocket. I quickly reached around and felt someone's hand. It was a twenty-something Romany (Gypsy) man and he had my wallet about halfway out of my pocket. I grabbed it, turned around, scowled at him (I'm 6'5") and he casually walked away. I'm sure he'd gotten off the tram with me and followed me to my door. I was stupid to have put my wallet in my back pocket in the first place. My Czech friends had told me that Czech people NEVER do that. I was lucky that time. I pass on this information to you because, as my mother used to say "a word to the wise is sufficient"! :-)