What is the basis for the Catechism saying that one can always be forgiven by perfect contrition come from? According to CCC 1452:

1452 When it arises from a love by which God is loved above all else, contrition is called &quot;perfect&quot; (contrition of charity). Such contrition remits venial sins; it also obtains forgiveness of mortal sins if it includes the firm resolution to have recourse to sacramental confession as soon as possible.51
51 Council of Trent (1551): DS 1677.

Thus, all sins, venial or mortal, can be forgiven by perfect contrition—that a sinner must sincerely repent and confess, and that's enough for God to forgive all sins, even the ones against Holy Spirit (as long as the sinner shows repentance).
What are, either Biblical, or infallible Catholic, statements, supporting this?
The answer is given in footnote 51 of what you quote:

Fourteenth Session of the Council of Trent (1551), "On the Most Holy Sacraments of Penance and Extreme Unction," ch. 4, "On Contrition":


  The Synod teaches…that…it sometimes happens that this contrition is perfect through charity, and reconciles man with God before this sacrament be actually received…


The Council of Trent is infallible because its documents were ratified by a pope.