Paper birch trees grow best in cool climates.  They prefer moist soils and can tolerate a range of soil types, doing best in acidic soils.  Has your area had unusually high temperatures? Has there been any drastic changes in the amount of rainfall?  Is this tree sitting in a lower area than the other tree, where water collects and drains too slowly?  Make sure when watering to only apply an amount that will drain and not saturate the soil.  Paper birch when stressed can attract insects called borers that feed under the bark and can kill the area above where they fed.  If this is the case you should see small exit holes where the borer emerged.  These would be found at the point where dead growth meets the healthy growth.  Either of these issues can cause the top portion of the plant to dieback.  https://www.na.fs.fed.us/spfo/pubs/howtos/ht_birch/ht_birch.htm

If the top buds do not open by end of spring, scratch the bark in this area to see if there is healthy green tissue under bark.  If it is brown then these twigs have died and it would be best to cut it back to healthy growth.  At this point it may be best to wait until the dormant season to do the pruning to avoid further attraction of borers to fresh cuts.  See the link above for more details on growing birch, maintaining the health of the plant and managing borer damage.