Can I have more than one relationship between two tables?
Yes. You have two different relationships here.


A one-to-one relationship between employees and header_maintenance_report via employee_id on each table.
A many-to-many relationship between employees and header_maintenance_report via the keys on detail_maintenance_report.


So long as you know what these two relationships represent (e.g. report author and report viewers) then there's no problem with that, however... I'd suggest you think carefully about naming. From your wording it's not clear exactly what the relationships represent but you might want to think twice about the use of "header" and "detail" in the table names as it sounds like the "detail" table is actually a joining table between the other two.

When using many-to-many relationships a common approach is to use the names of the two tables you're joining as the name for the join table, e.g.


employees
maintenance_reports
employees_to_maintenance_reports


Edit, see this example: http://sqlfiddle.com/#!9/03743/1