For what it’s worth. There are no rituals per se for “canonical closing,” and the term is something of a new one to me. There is nothing specified in the code at least.
But I think Br. Rich is pretty much on target. It is highly likely that what will be done will involve removing the Blessed Sacrament and any blessed or consecrated items from the church building.
Still it’s interesting (somewhat) to keep in mind that “parish” and “church” are not identical notions.
A parish is a certain community of the Christian faithful stably constituted in a particular church, and its pastoral care is entrusted to a priest as pastor under the authority of the diocesan bishop (c. 515). It has a public juridic personality in canon law (kind of like a civil corporation but underline kind of like!), so that it survives the coming and going of pastors and parishioners.
The term “church” can mean both a building set aside for divine worship by the faithful but also a portion of the people of God, such as a diocese, which is called a particular church in canon 515 above. In context though, a church is a sacred building destined for divine worship to which the faithful have a right of access for divine worship, especially its public exercise (c. 1214). It is an ecclesiastical property that belongs to the parish.
Now, parishes do usually have churches, but not always. Most do not when they are started. Instead, they use some other place for sacred worship. As well, a church in the sense of a sacred building could survive the closing of a parish. The church could continue as a place designated for sacred worship.
But in most cases today when parishes are closed, the church will no longer be used for sacred worship.
Two things would then be involved.
First, closing of the parish by the diocesan bishop (c. 515 §2). It would cease to exist as a public juridic person. This would mean distribution of its temporal goods, patrimonial rights and obligations according to law (c. 123). That would involve the removal and transfer or care of its property, records, assets, liabilities, etc. The precise distribution depends on a number of things.
Then possibly second, relegating its church to non sacred use (c. 1222), and hence the removal of the Blessed Sacrament and sacred objects. The altar would be secularized by a decree of the competent ordinary (c. 1212). If there are relics, I would certainly expect they would be removed…
Both kinds of closing are done by a decree of the diocesan bishop, who must first consult he presbyteral council, rather than by some kind of ritual. In practice, most dioceses have an additional and broader consultation or process. It’s always sad.
I don’t know, I would assume so.