Police won’t be interested. (and edited to ask why anyone thinks any authority would be – it’s logs and sticks in the woods and mountain biking may involve a few accidents..)
My tactic – just remove them every time and ride the most-often obstructed trails the most. It becomes a battle of wills.
I caught a guy at it on my local trails on morning. I had a fair but firm word, he was very defensive and sweary but not aggro. I told him there was likely to be more of us removing the logs than there were of him placing them and we thought it was a fun game. The logging stopped : )