The Bible does not tell us what type of wood the cross Jesus was crucified on was made of. Roman history does not go into specifics as to how the crosses were made or what type of wood was used. There is a legend that the cross was made of dogwood. This is unlikely considering the typical size of a dogwood tree. The legend of the dogwood tree, author unknown, is as follows:
In Jesus’ time, the dogwood grew
To a stately size and a lovely hue.
'Twas strong and firm, its branches interwoven.
For the cross of Christ its timbers were chosen.
Seeing the distress at this use of their wood
Christ made a promise which still holds good:
"Never again shall the dogwood grow
Large enough to be used so.
Slender and twisted, it shall be
With blossoms like the cross for all to see.
As blood stains the petals marked in brown,
The blossom’s center wears a thorny crown.
All who see it will remember Me
Crucified on a cross from the dogwood tree.
Cherished and protected, this tree shall be
A reminder to all of My agony."
Again, this is just a legend. It is a nice poem, but there is no biblical basis to it.