One quick question. What is the procedure state police follow if they are pursuing someone across state lines (suspect flees from home state to neighboring state line). Lets say going from Texas to New Mexico, can Texas DPS officer follow suspect into NM in pursuit?

What if suspect was simply speeding and state trooper tries to pull suspect over but suspect makes it into neighboring state line? Can the Texas DPS officer follow suspect into NM and issue ticket or make an arrest?

How does this apply to county sheriffs department in Texas, neighboring counties...ect?

Not planning on running from the cops or anything, just always wondered what this scenario entails.